Question

cost to own and operate a full-size truck
the graph below shows the cost to own and operate a full-size truck, y, in dollars, in terms of the miles the truck is driven, x.

a. find the slope of the line.
b. express the slope as a rate of change with the proper units attached.

a. the slope of the line is 0.30. (type an integer or a decimal. round to two decimal places as needed.)
b. express the slope as a rate of change with the proper units attached. select the correct choice below and fill in the answer box within your choice. (type an integer or a decimal. round to two decimal places as needed.)
a. the cost increases by $ 0.3 per mile driven.
b. the mileage increases by 0.30 miles per dollar spent.
c. the cost decreases by $ per mile driven.
d. the mileage decreases by miles per dollar spent.

Explanation:

Step1: Identify slope formula

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

Step2: Substitute given points

Use $(x_1,y_1)=(19000,5700)$ and $(x_2,y_2)=(40000,12000)$:
$m = \frac{12000 - 5700}{40000 - 19000}$

Step3: Calculate numerator and denominator

$m = \frac{6300}{21000}$

Step4: Simplify to find slope

$m = 0.30$

Step5: Interpret rate of change

Slope = $\frac{\text{Total Cost}}{\text{Miles Driven}}$, so it represents cost per mile.

Answer:

a. $0.30$
b. A. The cost increases by $\$0.3$ per mile driven.