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

Answer:

$y=-\frac{1}{4}x+40$

Step-by-step explanation:

Given

See attachment for graph

Required

Determine the equation of the line of best fit

First, calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph, we can have:

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

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

So, the slope is:

$m = \frac{25 -35}{60 - 20}$

$m = \frac{-10}{40}$

$m = -\frac{1}{4}$

The equation is then calculated as:

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

$y = -\frac{1}{4}(x - 20) + 35$

$y = -\frac{1}{4}x + 5 + 35$

$y=-\frac{1}{4}x+40$

Hence, the equation is: $y=-\frac{1}{4}x+40$