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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(a) How many miles does the train travel per gallon?

(b) What is the slope of the graph?

Answer 1

To determine the miles the train travels per gallon and the slope of the graph, we need to analyze the details provided about the graph.

(a) To find how many miles the train travels per gallon, we can use the data points from the graph. Typically, the x-axis will represent the gallons of fuel used, and the y-axis will represent the distance traveled. From the graph, if you have specific data points, such as:

• At \( x = 50 \) gallons, \( y = 102 \) miles
• At \( x = 100 \) gallons, \( y = 204 \) miles

We can calculate the miles per gallon using the slope formula, which is:

\[ \text{Slope (m)} = \frac{\Delta y}{\Delta x} \]

Taking two points from the graph:

1. \( (50, 102) \)
2. \( (100, 204) \)

Calculating the slope:

\[ \Delta y = 204 - 102 = 102 \] \[ \Delta x = 100 - 50 = 50 \]

Now, applying the slope formula:

\[ \text{Slope} = \frac{102}{50} = 2.04 \]

This means the train travels approximately 2.04 miles per gallon.

(b) The slope of the graph is the same value we calculated, indicating the rate of distance traveled per gallon of fuel consumed:

\[ \text{Slope of the graph} = \frac{102}{50} = 2.04 \]

Thus, the answers are:

(a) The train travels approximately 2.04 miles per gallon.
(b) The slope of the graph is 2.04.