We will decide who earns more per hour. To do so we will first find the constant of proportionality (unit rate) for both Amanda's and Petra's cases separately. Then we will compare the constants of proportionality. Let's begin with Amanda.

Amanda's Constant of Proportionality

Recall that a rate that tells the amount of one item in comparison to $1$ of another item is called a constant of proportionality. We know that the graph relating Amanda's earnings to the number of hours she babysits passes through the points $(0, 0)$ and $(4, 24) .$ Now we can draw a graph for Amanda's earnings over time by using these points.

To calculate the constant of proportionality in graphical representations, we can find the difference between any two pairs of coordinates. We already know two pairs of coordinates for the graph of Amanda's earnings.

From the graph we can see that the difference of the

x -

coordinates of the points is

4

and the difference of the

y -

coordinates is

24 .

Constant of Proportionality = \frac{2 4}{4} = 6 dollars per hour

Petra's Constant of Proportionality

Next we will find the constant of proportionality of Petra's earnings per hour. We are given a table that represents the relation of Petra's earnings to the number of hours she does yard work. By using the information in the table we can calculate Petra's earnings per hour.

	Petra's Earnings
Hours	$3$	$6$	$9$
Earnings $($)$	$15$	$30$	$45$
Earnings Per Hour $(\frac{$}{h})$	$\frac{1 5}{3} = 5$	$\frac{3 0}{6} = 5$	$\frac{4 5}{9} = 5$

Therefore, the constant of proportionality in Petra's case is $$ 5$ per hour.

Comparison

We found the constant of proportionality for both of the cases.

Amanda \underline{Constant of Proportionality} $ 6 per hour Petra \underline{Constant of Proportionality} $ 5 per hour

Amanda earns

$ 6

per hour, and Petra earns

$ 5

per hour. Therefore, Amanda earns more per hour.

Exercise