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.

Question

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 gallons does the train use per mile?
gallon(s)
(b) What is the slope of the graph?

Answer 1

To determine the fuel usage of the freight train based on the graph, we need to analyze the relationship between the distance traveled (x-axis) and the number of gallons used (y-axis). Since the problem states that fuel used varies directly with the distance traveled, we can find the slope, which represents the gallons of fuel used per mile and is constant in a linear relationship.

(a) To find the number of gallons used per mile:

1. Identify two points on the graph. For example, let's take (100 miles, 200 gallons) and (200 miles, 400 gallons).

2. Calculate the change in gallons and change in distance:

   • Change in gallons: \( 400 - 200 = 200 \) gallons
   • Change in distance: \( 200 - 100 = 100 \) miles

3. The gallons used per mile (or slope) is: \[ \text{slope} = \frac{\text{change in gallons}}{\text{change in distance}} = \frac{200 \text{ gallons}}{100 \text{ miles}} = 2 \text{ gallons/mile} \]

Therefore, the train uses 2 gallons per mile.

(b) The slope of the graph represents the same amount, which is the gallons of fuel used per mile. From our calculations:

The slope of the graph is 2.

In summary: (a) 2 gallons/mile (b) 2