Chapter 8.5, Problem 2CYU

To determine

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

Answer to Problem 2CYU

Hence, rate of change is 1$/pounds.

The linear relationship is proportional.

Explanation of Solution

Given:

  

Consider three points from the graph that shows relationship between number of pounds and total sales in dollars: (1,2) and (2,4)

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 height of plants with respect to change in number of weeks.

So, consider two points as: (1,2),(2,4)

Thus, constant rate of change is:

  $\begin{array}{l}Rateofchange=\frac{4-2}{2-1}\\ =\frac{2}{2}\\ \text{ = 1}\end{array}$

Hence, rate of change is 1$/pounds. . It means coffee is selling at the rate of $1 per pound.

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 $\frac{totalsales}{pounds}$ for each paired values.

For the point (1,2) the ratio is: $\frac{2}{1}=1$

And, for the point (2,4) the ratio is: $\frac{4}{2}=2$

Hence, ratio $\frac{totalsales}{pounds}$ is same for each paired value.

Thus, the linear relationship is proportional

Conclusion:

Therefore, rate of change is 1$/pounds. It means coffee is selling at the rate of $1 per pound.The linear relationship is proportional.