Exercise 13 Page 71

We are asked to find who charged more per hour. We can do this by finding the constant rate of change for each person's earnings and comparing the results. We will start with Ramona.

Let's analyze how Ramona's earnings change over time.

We can see that Ramona's earnings increase by $ 9 every hour. Let's use this information to write a unit rate, which is the same as the constant rate of change. Change in earnings/Change in time=$ 9/1hour We found that the constant rate of change for Ramona's earnings is $9 per hour. Now let's consider Josh's earnings. Take a look at the following graph.

Recall that if we are given two points that lie on a line, we can calculate the rate of change of the line using the following formula. Rate of change=Change in y/Change in x we can use any two points on the line. Let's use (1.10) and (2,20).

Now we can calculate the constant rate of change. Change in earnings/Change in time=$ 20-$ 10/(2-1)hours= $10/1hour We got that the constant rate of change for Josh's earnings is $10 per hour. Finally, let's compare the rates of change for Ramona and Josh. ccc Ramona & & Josh $ 9 per hour & < & $ 10 per hour Note that the constant rate of change for Josh's earnings is greater than for Ramona's. This means that Josh charges more per hour.