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.
y
50
100
150
200
250
300
350
400
x
50
100
150
200
250
300
350
400
0
Numberofgallonsused
Distancetraveled(miles)

(a) How many miles does the train travel per gallon?
mile(s)
(b) What is the slope of the graph?

Answer 1

To analyze the relationship between the number of gallons used and the distance traveled, we can derive the answers based on the information provided in the graph.

(a) To find how many miles the train travels per gallon, we need to determine the distance for one unit (gallon) of fuel. Since the relationship is direct, we can also infer this from the slope of the graph.

If we look for a pair of points on the graph to calculate the slope, let’s say we take two points:

1. (50 miles, 10 gallons)
2. (200 miles, 40 gallons)

Using these points:
- The change in distance (x) = 200 miles - 50 miles = 150 miles
- The change in gallons (y) = 40 gallons - 10 gallons = 30 gallons

The slope (which represents miles per gallon) is calculated as:
\[
\text{slope} = \frac{\text{change in y}}{\text{change in x}} = \frac{30}{150} = \frac{1}{5}
\]

This means the train travels 5 miles per gallon.

So answer (a) is 5 miles per gallon.

(b) The slope of the graph, which we calculated above, is also 5. The slope of the graph represents how many miles the train travels for each gallon of fuel used.

So answer (b) is also 5.