Question

A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 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.

Answer 1

Answer:

y(t) = 391 - 30t

Step-by-step explanation:

The weekly difference is 391-361 = 30

y(t) = 391 - 30t.

With t being the number of weeks.

Answer 2

Answer with explanation:

Number of Cars fixed in third week= 391 cars

Number of Cars fixed in 13th week = 361 cars

As it is given that reduction in the number of cars each week is linear.

Number of Week =X axis

Number of Cars fixed = Y axis

Taking two points as (3, 391) and (13,361) and finding the equation of linear function:

Equation of line Passing through two points  (3, 391) and (13,361) is given by:

      $\Rightarrow \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\Rightarrow \frac{y-361}{x-13}=\frac{391 -361}{3-13}\\\\\Rightarrow \frac{y-361}{x-13}=\frac{30}{-10}\\\\\Rightarrow \frac{y-361}{x-13}=-3\\\\\Rightarrow y-361=-3 x+39\\\\\Rightarrow 3 x+y=361+39\\\\\Rightarrow 3 x+y=400$

Equation of function  to show the number of cars seen each week by the mechanic is:

⇒ 3 x+y=400