Question

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. (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.) cost to own and operate a full - size truck \

$$\begin{array}{|c|c|}\\hline \\text{total cost (dollars)} & \\\\ \\hline 25,000 & \\\\ \\hline 20,000 & \\\\ \\hline 15,000 & (40000,12000) \\\\ \\hline 10,000 & \\\\ \\hline 5,000 & (19000,5700) \\\\ \\hline 0 & 0 \\\\ \\hline \\end{array}$$

miles driven: 0, 20,000, 40,000 \bigcirc a. the cost increases by $\square$ per mile driven. \bigcirc b. the mileage increases by $\square$ miles per dollar spent. \bigcirc c. the cost decreases by $\square$ per mile driven. \bigcirc d. the mileage decreases by $\square$ miles per dollar spent.

Explanation:

Step1: Identify slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Substitute given points

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

Step3: Calculate numerator and denominator

$12000-5700=6300$, $40000-19000=21000$
$m=\frac{6300}{21000}$

Step4: Simplify the fraction

$m=0.3$

Step5: Interpret slope as rate

Slope is cost per mile, positive so cost increases.

Answer:

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