{"id":249805,"date":"2022-09-19T16:17:43","date_gmt":"2022-09-19T14:17:43","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=249805"},"modified":"2025-05-16T16:38:25","modified_gmt":"2025-05-16T14:38:25","slug":"determiner-fonction-affine","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/determiner-fonction-affine\/","title":{"rendered":"Comment d\u00e9terminer une fonction affine ? \ud83d\udca1"},"content":{"rendered":"\n<p>En math\u00e9matiques, parmi les diff\u00e9rentes fonctions, il existe les fonctions affines. D\u2019ailleurs, au <a href=\"https:\/\/sherpas.com\/blog\/programme-maths-3eme\/\" data-type=\"post\" data-id=\"189758\">programme de 3e au coll\u00e8ge<\/a>, on te demande de bien les conna\u00eetre et de savoir les d\u00e9terminer dans des exercices. Mais alors, <strong>comment d\u00e9terminer une fonction affine<\/strong> ? \u00c7a tombe bien, c\u2019est justement le sujet de cette petite fiche de cours !<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"pour-commencer-un-peu-de-vocabulaire\">Pour commencer : un peu de vocabulaire<\/h2>\n\n\n\n<p>Tu as normalement appris qu\u2019une <strong>fonction<\/strong> <em>f<\/em> est un proc\u00e9d\u00e9 math\u00e9matique associant \u00e0 chaque nombre <em>x<\/em> un <span style=\"text-decoration: underline\" class=\"underline\">unique<\/span> nombre <em>y<\/em>. On note <em>f<\/em>(<em>x<\/em>) = <em>y<\/em> (ce qui se lit \u00ab <em>f de x \u00e9gal y <\/em>\u00bb).&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1600\" height=\"262\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?func=bound&amp;w=1024&amp;h=262\" alt=\"\" class=\"wp-image-265045\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=1600 1600w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=300 300w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=1024 1024w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=768 768w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=1536 1536w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=200 200w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=396 396w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=610 610w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-1.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=60 60w\" sizes=\"(max-width: 1600px) 100vw, 1600px\" \/><\/figure>\n\n\n\n<p><em>x<\/em> s\u2019appelle la <span style=\"text-decoration: underline\" class=\"underline\">variable<\/span> et les valeurs prisent par <em>x <\/em>s\u2019appellent les <span style=\"text-decoration: underline\" class=\"underline\">ant\u00e9c\u00e9dents<\/span>.&nbsp;<\/p>\n\n\n\n<p>\ud83d\udc49 <em>y<\/em> est le r\u00e9sultat de la transformation d\u2019un ant\u00e9c\u00e9dent <em>x <\/em>par la fonction <em>f<\/em> : il s\u2019appelle <span style=\"text-decoration: underline\" class=\"underline\">l\u2019image<\/span> de <em>x <\/em>par la fonction <em>f<\/em> et se note <em>f<\/em>(<em>x<\/em>). On \u00e9crit alors que : y = <em>f<\/em>(<em>x<\/em>).<\/p>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p><a href=\"https:\/\/sherpas.com\/blog\/comment-reviser-les-maths-examen\/\">Comment bien r\u00e9viser les maths <\/a>pour un examen ? \ud83d\udc4c<\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"definition-de-la-fonction-affine\">D\u00e9finition de la fonction affine <\/h2>\n\n\n\n<p>Une fonction affine est une fonction repr\u00e9sent\u00e9e par une droite (elle est lin\u00e9aire). Sa particularit\u00e9 par rapport aux autres fonctions est que son taux d&rsquo;accroissement est constant.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>m<\/em> et <em>p<\/em> sont deux nombres donn\u00e9s. La fonction <em>f<\/em> qui associe \u00e0 tout nombre <em>x<\/em> le nombre <em>mx <\/em>+ <em>p<\/em> est une <strong>fonction affine.<\/strong> Son expression alg\u00e9brique s\u2019\u00e9crit : &nbsp;<em>f<\/em>(<em>x<\/em>) = <em>mx <\/em>+ <em>p<\/em>.&nbsp;<\/li>\n\n\n\n<li><em>m<\/em> est le coefficient directeur de la fonction et on ajoute <em>p<\/em> au r\u00e9sultat.<\/li>\n\n\n\n<li>Par une fonction affine, chaque image a <span style=\"text-decoration: underline\" class=\"underline\">un seul ant\u00e9c\u00e9dent<\/span>.&nbsp;<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"569\" height=\"176\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png\" alt=\"\" class=\"wp-image-265046\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=569 569w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=300 300w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=200 200w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=396 396w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=60 60w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-2.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=565 565w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/figure>\n<\/div>\n\n\n<p>\ud83d\udc49 La repr\u00e9sentation graphique d\u2019une fonction affine est une <strong>droite<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Les <span style=\"text-decoration: underline\" class=\"underline\">ant\u00e9c\u00e9dents<\/span> d\u2019une valeur se lisent sur l\u2019axe des abscisses<\/li>\n\n\n\n<li><span style=\"text-decoration: underline\" class=\"underline\">L\u2019image<\/span> d\u2019une valeur se lit sur l\u2019axe des ordonn\u00e9es&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Exemple : La repr\u00e9sentation graphique de : <em>f<\/em>(<em>x<\/em>) = <em>3x <\/em>+ <em>2 <\/em>est<em> :<\/em><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"428\" height=\"426\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png\" alt=\"\" class=\"wp-image-265048\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=428 428w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=300 300w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=150 150w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=126 126w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=273 273w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=80 80w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=373 373w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=60 60w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-3.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=120 120w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/figure>\n<\/div>\n\n\n<p>On a bien l\u2019image de <em>0<\/em> qui est <em>2<\/em>, soit le point <em>A(0 ; 2)<\/em> et celle de <em>1<\/em> qui est <em>5<\/em>, donc le point <em>B(1 ; 5)<\/em>.<\/p>\n\n\n\n<p>Psst ! Les fonctions affines ne doivent pas \u00eatre un obstacle insurmontable : renforce tes comp\u00e9tences et gagne en confiance avec l&rsquo;aide d&rsquo;un <strong><a href=\"https:\/\/sherpas.com\/cours\/maths\">prof particulier de maths \u00e0 domicile<\/a> <\/strong>passionn\u00e9 et p\u00e9dagogue ! \u2728<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"comment-representer-une-fonction-affine\">Comment repr\u00e9senter une fonction affine ? <\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"a-laide-de-deux-points\">\u00c0 l\u2019aide de deux points<\/h3>\n\n\n\n<p>Tra\u00e7ons la courbe repr\u00e9sentative de la fonction affine <em>f<\/em>(<em>x<\/em>) = <em>2x <\/em>+ <em>1 <\/em>dans un rep\u00e8re.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>M\u00e9thode :<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>La repr\u00e9sentation graphique d\u2019une fonction affine est une <span style=\"text-decoration: underline\" class=\"underline\">droite<\/span>.<\/li>\n\n\n\n<li>Donc on d\u00e9termine deux points de la droite pour pouvoir la tracer.<\/li>\n\n\n\n<li>Pour cela, on choisit deux nombres quelconques et on calcule leur image.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>Solution :<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p>Une fonction affine est repr\u00e9sent\u00e9e par une droite.<\/p>\n\n\n\n<p>On choisit deux nombres quelconques, par exemple <em>\u20132 <\/em>et <em>3<\/em>. Puis on calcule leur image :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>f<\/em>(<em>\u20132<\/em>) =2<em>(\u20132) + 1 <\/em>= <em>\u20134 + 1 = \u20133 <\/em>donc la droite passe par le point&nbsp; <em>A(\u20132 ; -3).<\/em><\/li>\n\n\n\n<li><em>f<\/em>(<em>3<\/em>) = <em>2<\/em><em>3 + 1 <\/em>= <em>6 + 1 = 7 <\/em>donc la droite passe par le point&nbsp; <em>B(3 ; 7).<\/em><\/li>\n<\/ul>\n\n\n\n<p>La droite (<em>AB) <\/em>est donc la courbe repr\u00e9sentative <em>f.<\/em><\/p>\n\n\n\n<p>NB : Choisis des valeurs de <em>x <\/em>dont la diff\u00e9rence est significative afin d\u2019obtenir des points espac\u00e9s.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"504\" height=\"800\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png\" alt=\"\" class=\"wp-image-265049\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=504 504w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=189 189w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=79 79w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=171 171w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=277 277w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=234 234w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=237 237w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-4.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=38 38w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p><a href=\"https:\/\/sherpas.com\/blog\/comment-avoir-des-bonnes-notes\/\">Pour progresser en maths<\/a>, essaie notre m\u00e9thode du <a href=\"https:\/\/sherpas.com\/blog\/reverse-engeneering\/\">reverse engineering<\/a> ! \ud83d\udc4d<\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"avec-le-coefficient-directeur-et-de-lordonnee-a-lorigine\">Avec le coefficient directeur et de l\u2019ordonn\u00e9e \u00e0 l\u2019origine&nbsp;<\/h3>\n\n\n\n<p>Tra\u00e7ons dans un rep\u00e8re la courbe repr\u00e9sentative de la fonction affine <em>f <\/em>de param\u00e8tre <em>m = \u20132<\/em> et <em>p = 4.<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>M\u00e9thode :<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>On place le point <em>A(0 ; p)<\/em><\/li>\n\n\n\n<li>\u00c0 partir du point <em>A<\/em>, on place le point suivant \u00e0 l\u2019aide du coefficient directeur<\/li>\n\n\n\n<li>Pour cela, on avance d\u2019une unit\u00e9 sur l\u2019axe des abscisses et on monte de <em>p<\/em> sur l\u2019axe des ordonn\u00e9es si <em>p<\/em> est positif ou on descend de <em>p<\/em> si <em>p<\/em> est n\u00e9gatif.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>Solution :<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p>Une fonction affine est repr\u00e9sent\u00e9e par une droite.<\/p>\n\n\n\n<p><em>m <\/em>est le coefficient directeur de la droite et <em>p <\/em>est l\u2019ordonn\u00e9e \u00e0 l\u2019origine de la droite.<\/p>\n\n\n\n<p>Ici, <em>p = 4<\/em>, la droite passe donc par le point <em>A(0 ; 4).<\/em><\/p>\n\n\n\n<p>Ici, <em>m = \u20132<\/em> , or \u2013<em>2 &lt; 0 <\/em>donc on descend de <em>2<\/em> sur l\u2019axe des ordonn\u00e9es quand on avance de <em>1<\/em> sur l\u2019axe des abscisses. La droite passe donc par le point <em>A(1 ; 2)<\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"390\" height=\"484\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png\" alt=\"\" class=\"wp-image-265050\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=390 390w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=242 242w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=101 101w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=219 219w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=299 299w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-5.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=48 48w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/gEvab1ilmJjA82FaSV\/giphy.gif\" alt=\"\"\/><\/figure>\n<\/div>\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9mdW5uZWwtc3R1ZGVudC1xdWFsaWZpY2F0aW9u\" data-banner=\"2\" data-name=\"CPM1 Maths\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Louise2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Louise<\/p>                          <p class=\"push__teachers-school\">Mines ParisTech<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">24\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Nicolas2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Nicolas<\/p>                          <p class=\"push__teachers-school\">CentraleSup\u00e9lec<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">17\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Fabien2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Fabien<\/p>                          <p class=\"push__teachers-school\">T\u00e9l\u00e9com Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Cle\u0301mence2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Cl\u00e9mence<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Bastien2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Bastien<\/p>                          <p class=\"push__teachers-school\">Polytechnique<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Pierre2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Pierre<\/p>                          <p class=\"push__teachers-school\">ESSEC<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">16\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Simon2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Simon<\/p>                          <p class=\"push__teachers-school\">4e ann\u00e9e de m\u00e9decine<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Jade2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Jade<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">21\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Besoin d&rsquo;un <span style=\"color: #4cc583;\">prof particulier<\/span> de maths ? <span role=\"image\" aria-label=\"\u2728\">\u2728<\/span><\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos Sherpas sont l\u00e0 pour t&rsquo;aider \u00e0 progresser et prendre confiance en toi !<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        JE PRENDS UN COURS OFFERT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"comment-determiner-une-fonction-affine\">Comment d\u00e9terminer une fonction affine ?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"a-partir-de-deux-points-sur-un-graphisme\">\u00c0 partir de deux points sur un graphisme<\/h3>\n\n\n\n<p>Prenons le graphique ci-dessous comme exemple.&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"629\" height=\"469\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png\" alt=\"\" class=\"wp-image-265051\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=629 629w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=300 300w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=168 168w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=365 365w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=498 498w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-6.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=60 60w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><\/figure>\n<\/div>\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>\ud83d\udca1 M\u00e9thode<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <ul>\n<li>Pour d\u00e9terminer l\u2019ordonn\u00e9e \u00e0 l\u2019origine : on regarde la valeur au point d\u2019intersection entre l\u2019axe des ordonn\u00e9es et la droite<\/li>\n<li>On d\u00e9termine le signe du coefficient directeur : si <em>f<\/em> est croissante alors <em>m &gt; 0<\/em> et si <em>f<\/em> est d\u00e9croissante alors <em>m &lt; 0<\/em><\/li>\n<li>Pour d\u00e9terminer la valeur du coefficient directeur : on part d\u2019un point sur la droite et on avance d\u2019une unit\u00e9 sur l\u2019axe des abscisses, puis on regarde de combien il faut monter ou descendre sur l\u2019axe des ordonn\u00e9es pour rejoindre la droite.<\/li>\n<\/ul>\n\n        <\/div>\n              <\/section>\n\n\n\n<p class=\"has-text-align-center\"><strong>Solution :<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p>On regarde la valeur du point d\u2019intersection entre la droite et l\u2019axe des ordonn\u00e9es :&nbsp;<\/p>\n\n\n\n<p><em>f<\/em>(<em>0<\/em>) = <em>4 = p<\/em><\/p>\n\n\n\n<p>La droite est d\u00e9croissante, donc on sait que <em>m &lt; 0<\/em><\/p>\n\n\n\n<p>Quand on augmente <em>x<\/em> de 1, on constate que pour rejoindre la courbe, on descend de 3, donc :&nbsp;<em>m = \u2013 3<\/em>&nbsp;<\/p>\n\n\n\n<p>On en d\u00e9duit que l\u2019expression de <em>f<\/em> est : <em>f<\/em>(<em>x<\/em>) = <em>\u20133x + 4<\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"353\" height=\"436\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png\" alt=\"\" class=\"wp-image-265052\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=353 353w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=243 243w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=101 101w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=220 220w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=300 300w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-7.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=49 49w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n<section class=\"relance\">\n        <div >\n                        <div class=\"cursor-pointer\" data-toggle=\"modal\" data-target=\"#relance-modal-PCvns3za7A\">\n                <div class=\"relance__container\"\n                    >\n                                                                             <picture>\n                            <source srcset=\"https:\/\/sherpas.com\/content\/uploads\/2021\/10\/Maths-YT.png\" media=\"(min-width: 999px)\">\n                            <source srcset=\"https:\/\/sherpas.com\/content\/uploads\/2021\/10\/Maths-YT.png\" media=\"(max-width: 999px)\">\n                                <img decoding=\"async\"\n                                    src=\"https:\/\/sherpas.com\/content\/uploads\/2021\/10\/Maths-YT.png\"\n                                    alt=\"Comment vaincre la peur des maths ?\"\n                                >\n                            <\/picture>\n                                        <div class=\"relance__content\">\n                                                <div class=\"relance__title\"> <p>Les maths, quelle gal\u00e8re ! Tu veux gu\u00e9rir ta phobie de la mati\u00e8re ? Regarde cette vid\u00e9o \ud83d\udc47<\/p>\n<\/div>\n                                                <button type=\"button\"\n                                class=\"relance__button btn btn-white\">\n                            <svg>\n                                <use\n                                    xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#play\"\/>\n                            <\/svg>\n                            <span>ICI ! \ud83e\udd1d<\/span>\n                        <\/button>\n                    <\/div>\n                <\/div>\n            <\/div>\n                    <\/div>\n    <\/section>\n\n            <div class=\"modal-video modal fade\" id=\"relance-modal-PCvns3za7A\" tabindex=\"-1\" aria-hidden=\"true\">\n            <div class=\"modal-dialog\">\n                <div class=\"modal-content\">\n                    <iframe\n                        src=\"https:\/\/www.youtube.com\/embed\/PCvns3za7A\"\n                        title=\"YouTube video player\" frameborder=\"0\"\n                        allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\"\n                        allowfullscreen\n                    ><\/iframe>\n                <\/div>\n            <\/div>\n        <\/div>\n    \n\n\n<h3 class=\"wp-block-heading\" id=\"determiner-lexpression-dune-fonction-affine-a-partir-dun-calcul\">D\u00e9terminer l\u2019expression d\u2019une fonction affine \u00e0 partir d\u2019un calcul<\/h3>\n\n\n\n<p>Prenons la fonction <em>f<\/em> ci-dessous dont la droite passe par les points <em>A(2 ; 2)<\/em> et <em>B(6 ; 3).<\/em><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"760\" height=\"381\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png\" alt=\"\" class=\"wp-image-265053\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=760 760w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=300 300w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=200 200w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=396 396w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=610 610w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-8.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=60 60w\" sizes=\"(max-width: 760px) 100vw, 760px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center\"><strong>M\u00e9thode :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/10\/Capture-decran-2022-10-19-a-16.14.06-1024x229.png\" alt=\"\" class=\"wp-image-252139\"\/><\/figure>\n\n\n\n<p class=\"has-text-align-center\"><strong>Solution :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/10\/Capture-decran-2022-10-19-a-16.14.41-1024x202.png\" alt=\"\" class=\"wp-image-252140\"\/><\/figure>\n\n\n\n<p>On d\u00e9termine maintenant la valeur de l\u2019ordonn\u00e9e \u00e0 l\u2019origine, on a :&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/10\/Capture-decran-2022-10-19-a-16.15.12-1024x208.png\" alt=\"\" class=\"wp-image-252141\"\/><\/figure>\n\n\n\n<p>On peut donc en d\u00e9duire l\u2019expression de <em>f<\/em> \ud83d\udc47<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"698\" height=\"264\" src=\"https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/10\/Capture-decran-2022-10-19-a-16.16.31.png\" alt=\"\" class=\"wp-image-252143\" style=\"width:175px;height:66px\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/10\/Capture-decran-2022-10-19-a-16.16.31.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=698 698w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/10\/Capture-decran-2022-10-19-a-16.16.31.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=396 396w\" sizes=\"(max-width: 698px) 100vw, 698px\" \/><\/figure>\n<\/div>\n\n<section class=\"push \">\n        <div >\n            \n                                                <div class=\"push__container  qcd\" data-target=\"_self\" data-qcd=\"aHR0cHM6Ly9zaGVycGFzLmNvbS9mdW5uZWwtc3R1ZGVudC1xdWFsaWZpY2F0aW9u\" data-banner=\"2\" data-name=\"CPE1 brevet\" style=\"background-color: #F3FBF7\" >\n                                                                        <div class=\"push__teachers\">\n    <div class=\"d-flex justify-content-center d-md-none\">\n        <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\" alt=\"Logo Sherpas\">\n    <\/div>\n    <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Alma2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Alma<\/p>                          <p class=\"push__teachers-school\">ENS Paris-Saclay<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">24\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Noemie2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">No\u00e9mie<\/p>                          <p class=\"push__teachers-school\">M2 en droit \u00e0 Assas<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">19\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Bastien2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Bastien<\/p>                          <p class=\"push__teachers-school\">Polytechnique<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">26\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/David2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">David<\/p>                          <p class=\"push__teachers-school\">EDHEC<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">25\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Martin2x.jpg);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Martin<\/p>                          <p class=\"push__teachers-school\">HEC Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">23\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Emma2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Emma<\/p>                          <p class=\"push__teachers-school\">Dauphine<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                   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                                  <p class=\"push__teachers-price\">15\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Thibault2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Thibault<\/p>                          <p class=\"push__teachers-school\">ENS Paris Ulm<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">20\u20ac\/h<\/p>                     <\/div>\n                <\/div>\n                                            <div class=\"swiper-slide\">\n                    <div class=\"push__teachers-card\">\n                        <div\n                            class=\"push__teachers-profil\"\n                            \n                            style=\"background-image: url(https:\/\/sherpas.com\/content\/uploads\/2022\/01\/Antoine2x.png);\"\n                        >\n                    <\/div>\n                         <p class=\"push__teachers-name\">Antoine<\/p>                          <p class=\"push__teachers-school\">Sciences Po Paris<\/p>                                                     <div class=\"push__teachers-note\">\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                                    <svg  class=\"active\" >\n                                        <use\n                                            xlink:href=\"\/content\/themes\/sherpas-theme\/dist\/images\/sprite.svg#star\"\/>\n                                    <\/svg>\n                                                            <\/div>\n                                                 <p class=\"push__teachers-price\">18\u20ac\/h\/h<\/p>                     <\/div>\n                <\/div>\n                    <\/div>\n    <\/div>\n<\/div>\n                                                    <div class=\"push__content\">\n                                                            <div  class=\"d-none d-md-block\" >\n                                    <img decoding=\"async\" class=\"push__logo\" src=\"\/content\/themes\/sherpas-theme\/dist\/images\/logo.svg\"\n                                        alt=\"Logo Sherpas\">\n                                <\/div>\n                                                                                        <div class=\"push__title\"><p>Tu veux <span style=\"color: #000000;\">cartonner au brevet<\/span> ? \u2728<\/p>\n<\/div>\n                                                                                        <div class=\"push__text\"><p>Nos profs sont l\u00e0 pour t\u2019aider \u00e0 progresser !<\/p>\n<\/div>\n                                                        <div class=\"push__promo-button   \">\n                                                                                                    <div\n                                        class=\"btn btn-primary\"\n                                        style=\"color: ; border-color: ; background-color: \"\n\n                                    >\n                                        JE PRENDS UN COURS OFFERT !\n                                    <\/div>\n                                                            <\/div>\n                                                    <\/div>\n                                    <\/div>\n                                    <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"cas-particulier-de-la-fonction-affine-la-fonction-lineaire\">Cas particulier de la fonction affine : la fonction lin\u00e9aire<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"definition-de-la-fonction-lineaire\">D\u00e9finition de la fonction lin\u00e9aire<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Une fonction lin\u00e9aire est un cas particulier de la fonction affine.<\/li>\n\n\n\n<li>Pour un nombre<em> m<\/em>, la fonction<em> f <\/em>qui associe \u00e0 tout nombre <em>x<\/em> le nombre <em>mx<\/em> est une <strong>fonction lin\u00e9aire<\/strong>. Son expression alg\u00e9brique s\u2019\u00e9crit :<em> &nbsp;f<\/em>(<em>x<\/em>) = <em>mx<\/em><\/li>\n\n\n\n<li>Elle se caract\u00e9rise par une <span style=\"text-decoration: underline\" class=\"underline\">droite passant par l\u2019origine du rep\u00e8re<\/span><\/li>\n\n\n\n<li>Elle repr\u00e9sente une <strong>situation de proportionnalit\u00e9<\/strong> avec comme coefficient de proportionnalit\u00e9 le coefficient directeur de la fonction lin\u00e9aire, <em>m.<\/em><\/li>\n\n\n\n<li>Par une fonction lin\u00e9aire, chaque image a <span style=\"text-decoration: underline\" class=\"underline\">un seul ant\u00e9c\u00e9dent<\/span>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>Exemple<\/strong> : La repr\u00e9sentation graphique de <em>f<\/em>(<em>x<\/em>) = <em>3x<\/em> est :<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"333\" height=\"386\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png\" alt=\"\" class=\"wp-image-265054\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=333 333w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=259 259w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=108 108w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=235 235w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=320 320w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-9.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=52 52w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p>\ud83d\udc49 On a bien l\u2019image de <em>1<\/em> qui est <em>3<\/em>, soit le point <em>(1 ; 3)<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"determiner-le-coefficient-dune-fonction-lineaire\">D\u00e9terminer le coefficient d\u2019une fonction lin\u00e9aire<\/h3>\n\n\n\n<p>On consid\u00e8re la fonction lin\u00e9aire <em>f<\/em><em> <\/em>&nbsp;telle que <em>f<\/em>(<em>4<\/em>) = <em>2. <\/em>D\u00e9terminons son coefficient directeur <em>m.<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>M\u00e9thode :<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>f&nbsp; <\/em>est une fonction lin\u00e9aire donc <em>f<\/em>(<em>x<\/em>) = <em>mx<\/em><\/li>\n\n\n\n<li>On peut donc exprimer <em>f<\/em>(<em>3<\/em>) en fonction de <em>m<\/em> gr\u00e2ce \u00e0 son expression alg\u00e9brique&nbsp;<\/li>\n\n\n\n<li>Or on conna\u00eet la valeur de <em>f<\/em>(<em>3<\/em>) donc on peut r\u00e9soudre une \u00e9quation d\u2019inconnu <em>m.<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>Solution :<\/strong><\/p>\n\n\n\n<p>La fonction <em>f <\/em>est lin\u00e9aire donc&nbsp; <em>f<\/em>(<em>4<\/em>) = <em>2<\/em> peut s\u2019\u00e9crire sous la forme <em>f<\/em>(<em>x<\/em>) = <em>mx <\/em>&nbsp;<\/p>\n\n\n\n<p>Donc on peut remplacer les <em>x<\/em> dans l\u2019expression alg\u00e9brique par <em>4<\/em>, donc on a :&nbsp;&nbsp;<\/p>\n\n\n\n<p><em>f<\/em>(<em>4<\/em>) = <em>m*4&nbsp; <\/em>or &nbsp; <em>f<\/em>(<em>4<\/em>) = <em>2&nbsp; <\/em>donc &nbsp; <em>m*4 <\/em>= <em>2<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/sherpas.com\/blog\/content\/uploads\/2022\/10\/Capture-decran-2022-10-19-a-16.21.01-1024x205.png\" alt=\"\" class=\"wp-image-252146\" style=\"width:512px;height:103px\"\/><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/5bivKwxhVzshNk2Rjw\/giphy.gif\" alt=\"\"\/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"representer-une-fonction-lineaire\">Repr\u00e9senter une fonction lin\u00e9aire&nbsp;\ud83d\udd0d<\/h3>\n\n\n\n<p>Repr\u00e9sentons dans un rep\u00e8re la fonction lin\u00e9aire&nbsp; <em>f<\/em> telle que <em>f<\/em>(<em>x<\/em>) = <em>2x.<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>M\u00e9thode :<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Une fonction lin\u00e9aire se caract\u00e9rise par une <span style=\"text-decoration: underline\" class=\"underline\">droite passant par l\u2019origine<\/span> du rep\u00e8re.<\/li>\n\n\n\n<li>Donc on consid\u00e8re l\u2019origine du rep\u00e8re comme un premier point, et il suffit de trouver un second point de cette droite pour pouvoir la tracer.<\/li>\n\n\n\n<li>Pour cela, on choisit un nombre quelconque et on calcule son image.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>Solution :<\/strong><\/p>\n\n\n\n<p>Une fonction lin\u00e9aire est repr\u00e9sent\u00e9e par une droite passant par l\u2019origine <em>O<\/em> du rep\u00e8re. On choisit un nombre quelconque, par exemple <em>1 <\/em>et on calcule son image :<\/p>\n\n\n\n<p><em>f<\/em>(<em>1<\/em>) = <em>2<\/em><em>1 <\/em>= <em>2&nbsp; <\/em>donc la droite passe aussi par le point&nbsp; <em>A(1 ; 2).<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center\">La droite (<em>OA) <\/em>est donc la courbe repr\u00e9sentative <em>f.<\/em><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"471\" height=\"417\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png\" alt=\"\" class=\"wp-image-265055\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=471 471w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=300 300w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=141 141w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=307 307w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=419 419w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-10.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=60 60w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><\/figure>\n<\/div>\n\n<section class=\"you-know\">\n                <div class=\"you-know__title\"><p>Tips \ud83d\udca1<\/p>\n<\/div>\n                        <div class=\"you-know__text\">\n            <p>Selon l\u2019\u00e9chelle de ton graphique, tu peux <strong>choisir des points plut\u00f4t \u00e9loign\u00e9s<\/strong> pour plus de pr\u00e9cision. Tu peux aussi placer un troisi\u00e8me point pour v\u00e9rifier l\u2019alignement.<\/p>\n\n        <\/div>\n              <\/section>\n\n\n<section class=\"read-also\">\n    <p class=\"read-also__title\">\u00c0 lire aussi<\/p>\n            <div class=\"read-also__list\">\n            <p>D\u00e9couvre le <a href=\"https:\/\/sherpas.com\/blog\/programme-maths-seconde\/\">programme de maths en Seconde<\/a> pour prendre de l&rsquo;avance \ud83d\udd0d<\/p>\n\n        <\/div>\n    <\/section>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"synthese-sur-les-fonctions-affines\">Synth\u00e8se sur les fonctions affines \ud83d\udcad<\/h2>\n\n\n\n<p>Pour conclure cet article, voil\u00e0 un petit rappel sur les fonctions. Car souviens-toi bien que pour <strong>d\u00e9terminer une fonction affine<\/strong>, il faut d\u2019abord bien conna\u00eetre son sujet ! \ud83d\ude09 Et si apr\u00e8s tout \u00e7a le concept de fonction affine te semble flou, un <strong><a href=\"https:\/\/sherpas.com\/cours\/maths\/online\">cours particulier de maths en visio<\/a><\/strong> avec nos Sherpas s&rsquo;impose ! \ud83e\uddd0<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"689\" height=\"418\" src=\"https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png\" alt=\"\" class=\"wp-image-265056\" srcset=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=689 689w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=300 300w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=200 200w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=396 396w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=288 288w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=610 610w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=265 265w, https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/content\/uploads\/2023\/09\/determiner-fonction-affine-11.png?q=85&amp;force_format=webp&amp;org_if_sml=1&amp;w=60 60w\" sizes=\"(max-width: 689px) 100vw, 689px\" \/><\/figure>\n<\/div>\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;249805&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;21&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;4&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;Tu as aim\u00e9 cet article ?&quot;,&quot;legend&quot;:&quot;4\\\/5 - (21 votes)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Comment d\u00e9terminer une fonction affine ? \ud83d\udca1&quot;,&quot;width&quot;:&quot;113.5&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 113.5px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            4\/5 - (21 votes)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>En math\u00e9matiques, parmi les diff\u00e9rentes fonctions, il existe les fonctions affines. D\u2019ailleurs, au programme de 3e au coll\u00e8ge, (&#8230;)<\/p>\n","protected":false},"author":158,"featured_media":252148,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":true,"footnotes":""},"category":[803,810],"tag":[77,770,352],"class_list":["post-249805","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-college","tag-fiche-revision","tag-troisieme"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/249805","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/158"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=249805"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/249805\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/252148"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=249805"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=249805"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=249805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}