Question

Cars lose value the farther they are driven. A random sample of 11 cars for sale was taken. All 11 cars were the same make and model. A line was fit to the data to model the relationship between how far each car had been driven and its selling price.

Answer 1

`y=-(1)/(4)x+40`

Explanation:

Given

See attachment for graph

Required

Determine the equation of the line of best fit

First, calculate the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

From the graph, we can have:

`(x_1,y_1) = (20,35)`

`(x_2,y_2) = (60,25)`

So, the slope is:

`m = (25 -35)/(60 - 20)`

`m = (-10)/(40)`

`m = -(1)/(4)`

The equation is then calculated as:

`y = m(x - x_1) + y_1`

`y = -(1)/(4)(x - 20) + 35`

`y = -(1)/(4)x + 5 + 35`

`y=-(1)/(4)x+40`

Hence, the equation is:
`y=-(1)/(4)x+40`