Chapter 8.5, Problem 12PPS

To determine

whether each statement is true or false.

Answer to Problem 12PPS

Thus, the statement is true

Explanation of Solution

Given:

A proper linear relationship exists

  

Calculation:

Consider three points from the graph that shows relationship between total cost and number of rooms: $(1,110),(1,5,120)$ and $(2,140)$

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 $\frac{totalcost}{numberofrooms}$ for each paired values.

For the point $(1,110)$ the ratio is: $\frac{110}{1}=110$

And, for the point $(1,5,120)$ the ratio is: $\frac{120}{15}=80$

And also, for the point $(2,140)$ the ratio is: $\frac{140}{2}=70$

Hence, ratio $\frac{totalcost}{numberofrooms}$ is not same for each paired value.

Thus, the statement is false that a proportional linear relationship exists.

Conclusion:

Thus, the statement is true