Question

Find the rate of change for the following set of data. Linear behavior

Answer 1

Since the table shows points with linear behavior, we can find the rate of change (slope) by taking a pair of points. For instance, if we choose the points

`\begin{gathered} (x_1,y_1)=(7.15,26) \\ (x_2,y_2)=(7.24,71) \end{gathered}`

the rate of change is given by

`(y_2-y_1)/(x_2-x_1)=\frac{(71-26)\text{ people}}{(7\colon24-7\colon15\text{) minutes}}`

which gives

`(y_2-y_1)/(x_2-x_1)=\frac{45\text{ people}}{9\text{ minutes}}=5\text{ people per minute}`

Therefore, the rate of change is: 5 people per minute.