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

Question

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

Answer 1

To analyze the relationship between the distance traveled by the freight train and the number of gallons of fuel used, we can use the information from the graph. Since the graph shows a direct variation between distance and fuel usage, the slope will be constant.

(a) To find out how many gallons the train uses per mile, we can use the slope of the graph, which represents the rate of change (in this context, gallons of fuel per mile).

Let's say the slope is calculated as follows (assuming you have data points from the graph):

1. Select two points from the graph. For example, at \( (100, 200) \) and \( (200, 400) \):

   • The y-values represent distance (miles).
   • The x-values represent gallons used.

2. Calculate the slope (gallons per mile) using the formula for slope:

\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{400 - 200}{200 - 100} = \frac{200}{100} = 2 \]

This result means that the freight train uses 2 gallons per mile.

(b) The slope of the graph is therefore 2, indicating that for every mile traveled, the train uses 2 gallons of fuel.