Chapter 8.5, Problem 4PPS

To determine

To find: the constant rate of change and determine whether a proportional linear relationship exists between the two quantities.

Answer to Problem 4PPS

Hence, rate of change is $\frac{1}{2}$ $ /$.

The linear relationship is not proportional.

Explanation of Solution

Given:

  

Consider three points from the graph that shows relationship between sales and cost: (10,15),(20,20) and (30,25)

Calculation:

In order to find constant rate of change, take any two points and use the formula for rate of change.

  $Rateofchange=\frac{changeiny}{changeinx}$

It means rate of change is change in cost with respect to change in sales.

So, consider two points as: (10,15), (20,20)

Thus, constant rate of change is:

  $\begin{array}{l}Rateofchange=\frac{20-15}{20-10}\\ =\frac{5}{10}\\ \text{ = }\frac{1}{2}\end{array}$

Hence, rate of change is $\frac{1}{2}$ $ /$. It means that plant is growing at the rate of $ $\frac{1}{2}$ per dollar.

Linear relationships are called proportional if the ration of each non zero y -value compared to corresponding x -value is the same.

Now, it means that calculate ratio $\frac{\cos t}{sale}$ for each paired values.

For the point (10,15) the ratio is: $\frac{15}{10}=1.5$

And, for the point (20,20) the ratio is: $\frac{20}{20}=1$

And also, for the point (30,25) the ratio is: $\frac{25}{30}=\frac{5}{6}$

Hence, ratio $\frac{\cos t}{sale}$ is not same for each paired value.

Thus, the linear relationship is not proportional

Conclusion:

Therefore, rate of change is $\frac{1}{2}$ $ /$. It means that plant is growing at the rate of $ $\frac{1}{2}$ per dollar.The linear relationship is not proportional.