Question

The distance y (in miles) that Train A travels in x hours is represented by the equation y = 76x. The graph shows the distance that Train B travels. Is Train A faster or slower than Train B?

Answer 1

The slope of a Line

If we represent the distance y in terms of the time x, the slope of the line represents the speed of the object.

Concretely, if

y = mx

is the equation of the line, then m is the speed of the train.

Train A's motion is represented by:

y = 76x

This means that the speed of train A is 76 miles per hour.

We now need to find the speed of train B. That will be calculated from the graph of its motion. Select two points from it, for example, (0,0) and (1,74).

Calculate the slope with the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting:

$\begin{gathered} m=\frac{74-0}{1-0} \\ \text{Calculating:} \\ m=74\text{ mph} \end{gathered}$

The speed of train B is 74 miles per hour.

This means that Train A is faster than Train B