Question

a freight train is carrying goods across the country. the number of gallons of fuel it has used varies directly with the distance it has traveled. see the graph below.

(a) how many miles does the train travel per gallon?
\boxed{} mile(s)

(b) what is the slope of the graph?
\boxed{}

Explanation:

Step1: Pick a point from the graph

Choose the point $(50, 400)$ where distance $x=50$ miles, fuel $y=400$ gallons.

Step2: Calculate miles per gallon

Divide distance by gallons.
$\frac{50}{400} = \frac{1}{8}$

Step3: Calculate slope of the graph

Slope is $\frac{\text{change in } y}{\text{change in } x}$, use the same point.
$\frac{400}{50} = 8$

Answer:

(a) $\frac{1}{8}$ mile(s)
(b) $8$