a) Parmi les règles suivantes, lesquelles représentent des fonctions affines? y=x^(2)+3 y=(-2x)/(5)+(1)/(8) y=((x+7))/(3) y=4x+(3)/(7) y=(x)/(4) y=(3)/(x) y=(-8)/(x)-9 y=5(x-2)^(2) y=-5x+12 b) Pour chacune des fonctions affines que tu as trouvées en a), détermine le taux de variation et la valeur initiale. 2. Écris la règle d'une fonction affine passant par les points suivants. a) (1,3) et (3,5) d) (2,1) et (6,4) b) (2,3) et (-1,6) e) (-1,2) et (3,4) c) (-1,-2) et (-5,-10) f) ((1)/(2),(8)/(9)) et ((7)/(4),(8)/(9)) 3. Une droite passe par le point (1,-3) . Trouve la règle des fonctions dont la pente de la droite est : a) 0 b) 4 c) -1 d) (3)/(4)

<p><br />1. a) Affine functions are of the form \(f(x) = ax + b\), where \(a\) and \(b\) are constants. Among the given equations, \(y=\frac{-2 x}{5}+\frac{1}{8}\), \(y=\frac{(x+7)}{3}\), and \(y=-5 x+12\) are affine functions.<br /> b) For \(y=\frac{-2 x}{5}+\frac{1}{8}\), the rate of change is \(\frac{-2}{5}\) and the initial value is \(\frac{1}{8}\). For \(y=\frac{(x+7)}{3}\), the rate of change is \(\frac{1}{3}\) and the initial value is \(\frac{7}{3}\). For \(y=-5 x+12\), the rate of change is \(-5\) and the initial value is \(12\).<br /> <br />2. To find the rule of an affine function passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula \(y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)\). Applying this formula to each pair of points, we get the respective affine functions.<br /><br />3. To find the rule of a function with a given slope \(m\) that passes through the point \((1, -3)\), we use the point-slope form \(y-y_1 = m(x-x_1)\). Substituting \(m\) and \((1, -3)\) into the equation, we get the respective functions.<br /></p>