Chapter 8.5, Problem 6PPS

To determine

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

Answer to Problem 6PPS

Hence, rate of change is 5lb/number of 1 iron weights. The linear relationship is proportional.

Explanation of Solution

Given:

  

Consider three points from the graph that shows relationship between iron weights and total weights: (2,10),(4,20) and (6,30)

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 total weights with respect to change in number of iron weights.

So, consider two points as: (2,10), (4,20)

Thus, constant rate of change is:

  $\begin{array}{l}Rateofchange=\frac{20-10}{4-2}\\ =\frac{10}{2}\\ \text{ = }5\end{array}$

Hence, rate of change is 5lb/number of 1 iron weights.

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 $\frac{totalweights}{Numberofironweights}$ for each paired values.

For the point (2,10) the ratio is: $\frac{10}{2}=5$

And, for the point (4,20) the ratio is: $\frac{20}{4}=5$

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

Hence, ratio $\frac{totalweights}{Numberofironweights}$ is same for each paired value.

Thus, the linear relationship is proportional.

Conclusion:

Therefore, rate of change is 5lb/number of 1 iron weights. The linear relationship is proportional.