Chapter 8.5, Problem 5PPS

To determine

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

Answer to Problem 5PPS

Hence, rate of change is 500 mile /hour.

The linear relationship is proportional.

Explanation of Solution

Given:

  

Consider three points from the graph that shows relationship between time and distance: (2,1000),(4,2000) and (6,3000)

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: (2,1000), (4,2000)

Thus, constant rate of change is:

  $\begin{array}{l}Rateofchange=\frac{2000-1000}{4-2}\\ =\frac{1000}{2}\\ \text{ = }500\end{array}$

Hence, rate of change is 500 mile /hour. It means that airplane travels 500 miles per hour.

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 $\frac{dis\tan ce}{time}$ for each paired values.

For the point (2,1000) the ratio is: $\frac{1000}{2}=500$

And, for the point (4,2000) the ratio is: $\frac{2000}{4}=500$

And also, for the point (6,3000) the ratio is: $\frac{3000}{6}=500$

Hence, ratio $\frac{dis\tan ce}{time}$ is same for each paired value.

Thus, the linear relationship is proportional.

Conclusion:

Therefore, rate of change is 500 mile /hour. It means that airplane travels 500 miles per hour.The linear relationship is proportional.