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{"id":250,"date":"2020-11-11T20:30:05","date_gmt":"2020-11-11T20:30:05","guid":{"rendered":"http:\/\/ms.iaca.fr\/?p=250"},"modified":"2020-11-17T07:31:41","modified_gmt":"2020-11-17T07:31:41","slug":"deux-droites-sur-un-repere","status":"publish","type":"post","link":"http:\/\/ms.iaca.fr\/deux-droites-sur-un-repere","title":{"rendered":"Deux droites sur un rep\u00e8re"},"content":{"rendered":"\n
\"\"<\/figure><\/div>\n\n\n\n

Compl\u00e8te le tableau suivant :
<\/p>\n\n\n\n

x<\/td>-2<\/td>0<\/td>3<\/td> <\/td>5<\/td><\/tr>
Image par la droite bleue<\/td> <\/td> <\/td> <\/td> <\/td> <\/td><\/tr>
Image par la droite rouge<\/td> <\/td> <\/td> <\/td>5<\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Pour retrouver les images, il faut lire les informations sur l’axe horizontal, remonter jusqu’\u00e0 la droite concern\u00e9e, et regarder la valeur associ\u00e9e sur l’axe vertical. Nous trouvons pour les 3 premi\u00e8res colonnes:
droite bleue : (-2 ; -1<\/strong>) , (0 ; 1<\/strong> ) , (3 ; 4<\/strong>)
droite rouge : (-2 ; 2<\/strong>) , (0 ; 3<\/strong> ) , (3 ; 4,5 <\/strong>)

Pour le point suivants : il faut lire l’ant\u00e9c\u00e9dant de la droite rouge pour en d\u00e9duire l’image de la droite bleue. L’ant\u00e9c\u00e9dent est 4, et l’image de 4 par la droite bleue est 5.

Pour le dernier point, il faut prolonger le rep\u00e8re, ou trouver l’\u00e9quation de chaque droite pour remplacer la valeur x par 5. Nos trouvons:
droite bleue : (5 ; 6 <\/strong>)
droite rouge : (5 ; 5,5 <\/strong>)
<\/p>\n\n\n\n

Repr\u00e9sente<\/strong> la droite d\u2019\u00e9quation 0,5x<\/code><\/em><\/p>\n\n\n\n

Cette \u00e9quation est une \u00e9quation de droite. Il faut identifier deux points facilement identifiable et les relier pour cr\u00e9er une droite.
Il faut remplacer x par des valeurs au choix. Par exemple : (0 ; 0 ) , ( 1 ; 0,5 ) , ( 4 ; 2 ) , etc…<\/p>\n\n\n\n

Retrouve<\/strong> l\u2019\u00e9quation des droites bleues et rouge et v\u00e9rifie alg\u00e9briquement la solution pour x = 5<\/p>\n\n\n\n

Il faut identifier l’ordonn\u00e9e \u00e0 l’origine et le coefficient directeur:

droite bleue <\/strong>: y = x+1 ;
si x = 5<\/span> ; y<\/span> = 5<\/span> + 1 = 6<\/span>

droite rouge<\/strong> : y = 0,5x + 3 ;
si x = 5<\/span> , y<\/span> = 0,5 \u00d7 5<\/span> + 3 = 5,5<\/span>
On retrouve bien les r\u00e9sultats du tableau pr\u00e9c\u00e9dent.<\/p>\n","protected":false},"excerpt":{"rendered":"

Compl\u00e8te le tableau suivant : x -2 0 3   5 Image par la droite bleue           Image par la droite rouge       5   Pour retrouver les images, il faut lire les informations sur l’axe horizontal, remonter jusqu’\u00e0 la droite concern\u00e9e, et regarder la valeur associ\u00e9e sur l’axe … <\/p>\n