Question

a) what is the slope of the line?
50
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1. what does the slope tell you?

the train travels miles per hour.
(graph: distance (mi) on y - axis, time (h) on x - axis, line passing through origin and other points)

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line is given by \( m=\frac{\Delta y}{\Delta x} \), where \( \Delta y \) is the change in \( y \)-values and \( \Delta x \) is the change in \( x \)-values.

Step2: Identify points on the line

From the graph, when \( x = 1 \) (time in hours), \( y = 50 \) (distance in miles); when \( x = 2 \), \( y = 100 \). So \( \Delta y=100 - 50 = 50 \), \( \Delta x=2 - 1 = 1 \).

Step3: Calculate slope

Using the slope formula, \( m=\frac{50}{1}=50 \). The slope represents the rate of change of distance with respect to time, which is speed. So the train travels 50 miles per hour.

Answer:

50