Chapter SH, Problem 8.5.2EP

To determine

To calculate: To find the constant rate of change for the linear function and interpret its meaning

Answer to Problem 8.5.2EP

Rate of change is $12$

Explanation of Solution

Given information: Linear function is

Filling a pool
Time (min)	Volume (gal)
x	y
5	60
10	120
15	180
20	240

Formula Used:

Rate of change of function is calculated as

  $Rateofchange=\frac{Changeiny-coordinates}{Changeinx-coordinates}$

Calculation:

Linear function is given

Filling a pool
Time (min)	Volume (gal)
x	y
5	60
10	120
15	180
20	240

Rate of change is calculated as

  $Rateofchange=\frac{Changeiny-coordinates}{Changeinx-coordinates}$

Thus, rate of change of given function is

  $\begin{array}{l}Rateofchange=\frac{120-60}{10-5}\\ Rateofchange=\frac{60}{5}\\ Rateofchange=12\end{array}$

Since the rate of change is positive, this means that value of y-coordinate increases with the increase in x-coordinate.

Here, magnitude of rate of change is $12$ , which means for every $1$ minute increase in time there is increase in volume by $12$ gallons

Conclusion:

Hence, rate of change is $12$