Question

(02.04 mc) a car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. during week 2 of the recall, the manufacturer fixed 192 cars. in week 4, manufacturer fixed 184 cars. assume that the reduction in the number of cars each week is linear. write an equation in function form to show the number of cars seen each week at the mechanic. (1 point) f(x)=4x + 200 f(x)=2x + 192 f(x)=-4x + 200 f(x)=-2x + 192

Explanation:

Step1: Find the slope

The slope $m$ of a linear - function $y = mx + b$ can be found using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the week number and $y$ be the number of cars fixed. We have the points $(x_1,y_1)=(2,192)$ and $(x_2,y_2)=(4,184)$. Then $m=\frac{184 - 192}{4 - 2}=\frac{-8}{2}=-4$.

Step2: Find the y - intercept

We use the point - slope form $y - y_1=m(x - x_1)$ and then convert it to the slope - intercept form $y=mx + b$. Using the point $(2,192)$ and $m=-4$, we have $y-192=-4(x - 2)$. Expand the right - hand side: $y-192=-4x + 8$. Add 192 to both sides to get $y=-4x+200$. In function form $f(x)=-4x + 200$.

Answer:

C. $f(x)=-4x + 200$