Chapter SH, Problem 8.5.1EP

To determine

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

Answer to Problem 8.5.1EP

Rate of change is $-0.5$

Explanation of Solution

Given information: Linear function is

  

Formula Used:

Rate of change of function is calculated as

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

Calculation:

Linear function is given

  

From the graph, points on graph are $\left(8,12\right)$ and $\left(16,8\right)$

Rate of change is calculated as

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

Thus, rate of change of given function is

  $\begin{array}{l}Rateofchange=\frac{8-12}{16-8}\\ Rateofchange=\frac{-4}{8}\\ Rateofchange=-\frac{1}{2}\\ Rateofchange=-0.5\end{array}$

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

Here, magnitude of rate of change is $0.5$ , which means for every increase of $8$ cookies there is decrease in flour by $4$ units

Conclusion:

Hence, rate of change is $-0.5$