Question

(02.04 mc)
a car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. during week 10 of the recall, the manufacturer fixed 200 cars. in week 15, the manufacturer fixed 175 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 by the mechanic.

○ f(x) = 5x + 250
○ f(x) = -5x + 250
○ f(x) = 10x + 200
○ f(x) = -10x + 200

Explanation:

Step1: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(x_1 = 10,y_1=200,x_2 = 15,y_2 = 175\).
\(m=\frac{175 - 200}{15 - 10}=\frac{-25}{5}=- 5\)

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Substitute \(m=-5,x_1 = 10,y_1 = 200\) into \(y - y_1=m(x - x_1)\)
\(y-200=-5(x - 10)\)
\(y-200=-5x + 50\)
\(y=-5x+250\)
In function form \(f(x)=-5x + 250\)

Answer:

\(f(x)=-5x + 250\) (the second option)