Chapter 8.5, Problem 7PPS

To determine

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

Answer to Problem 7PPS

Hence, rate of change is -1 ticket available/ticket sold.

The linear relationship isnot proportional.

Explanation of Solution

Given:

  

Consider three points from the graph that shows relationship between ticket sold and number of tickets available: (20,50),(40,30) and (60,10)

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 tickets available with respect to change in tickets sold.

So, consider two points as: (20,50), (40,30)

Thus, constant rate of change is:

  $\begin{array}{l}Rateofchange=\frac{30-50}{40-20}\\ =\frac{-20}{20}\\ \text{ = }-\text{1}\end{array}$

Hence, rate of change is -1 ticket available/tickets sold.

It means for each ticket sold, there is 1 less ticket to buy.

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

Now, it means that calculate ratio $\frac{\text{ticket available}}{ticketssold}$ for each paired values.

For the point (20,50) the ratio is: $\frac{50}{20}=\frac{5}{2}$

And, for the point (40,30) the ratio is: $\frac{30}{40}=\frac{3}{4}$

And also, for the point (60,10) the ratio is: $\frac{10}{60}=\frac{1}{6}$

Hence, ratio $\frac{\text{ticket available}}{ticketssold}$ is not same for each paired value.

Thus, the linear relationship is not proportional.

Conclusion:

Therefore, rate of change is -1 ticket available/ticket sold. The linear relationship isnot proportional.