Question

The graph show the distance is traveled by two bikers riding at constant rates please help me find which table the unit rate that matches with each graph thank you

Answer 1

The rate is given by the slope which is defined by:

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

The first line passes throught the points (0,0) and (21,1); hence its rate is:

$\begin{gathered} m=\frac{21-0}{1-0} \\ m=\frac{21}{1} \\ m=21 \end{gathered}$

Therefore, the rate of change of the first line is 21 mph.

Using the points given for the second line we have:

$\begin{gathered} m=\frac{68-51}{4-3} \\ m=\frac{17}{1} \\ m=17 \end{gathered}$

Therefore, the rate of change of the second line is 17 mph.