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The rate of change for our given situation is 7 miles per hour.
What is a slope?
Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line.
We have been given that you run 7 miles in one hour and 21 miles in three hours. We are asked to find the rate of change for our given situation.
We will use slope formula to solve our given problem as slope represents rate of change of a function.
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Where,
[tex]y_{2} -y_{1}[/tex] = Difference between two y-coordinates,
[tex]x_{2} -x_{1}[/tex] = Difference between x-coordinates of same two y-coordinates.
Since number of miles is dependent on number of hours, so number of miles will be our y values and number of hours will be our x values.
Upon substituting coordinates of points (1,7) and (3,21) in slope formula we will get,
Slope = [tex]\frac{21-7}{3-1}[/tex]
Slope = [tex]\frac{14}{2}[/tex]
Slope = 7
Therefore, the rate of change for our given situation is 7 miles per hour.
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