Given:
Table of values.
The train travels at a constant speed.
To find:
The speed of train in miles per hour.
Solution:
From the given table consider any two points, i.e., (0.5,22.5) and (1,45).
The train travels at a constant speed. It means, there is a linear relationship between time and distance.
The average rate of change (Slope) of a linear relationship is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{45-22.5}{1-0.5}[/tex]
[tex]m=\dfrac{22.5}{0.5}[/tex]
[tex]m=\dfrac{225}{5}[/tex]
[tex]m=45[/tex]
So, average rate of change in distance with respect to time is 45.
Therefore, the speed of the train is 45 miles per hour.
