The table shows the linear relationship between the number of hours Georgia worked at the tutoring center, x, and the amount of money Georgia earned, y.

Question

Georgia's Earnings

Number of Hours Worked 3.2 4.7 6.2 7.7
Amount Earned $51.20 $75.20 $99.20 $123.20

What is the rate of change and what does it mean?
Responses
A The rate of change is 24. Georgia earns $24 per hour that she tutors.The rate of change is 24. Georgia earns $24 per hour that she tutors.
B The rate of change is 1.5. Georgia earns $1.50 per hour that she tutors.The rate of change is 1.5. Georgia earns $1.50 per hour that she tutors.
C The rate of change is 16. Georgia earns $16 per hour that she tutors.The rate of change is 16. Georgia earns $16 per hour that she tutors.
D The rate of change is 8. Georgia earns $8 per hour that she tutors.

Answer 1

To find the rate of change (or the slope) of the linear relationship between the number of hours Georgia worked and the amount of money she earned, we can use the formula:

\[ \text{Rate of Change} = \frac{\Delta y}{\Delta x} \]

We can select any two points from the table to calculate the rate of change. For example, we can use the points (3.2, 51.20) and (4.7, 75.20).

Calculating the change in \(y\) (amount earned):

\[ \Delta y = 75.20 - 51.20 = 24 \]

Calculating the change in \(x\) (number of hours worked):

\[ \Delta x = 4.7 - 3.2 = 1.5 \]

Now we can calculate the rate of change:

\[ \text{Rate of Change} = \frac{24}{1.5} = 16 \]

This means that Georgia earns $16 for each hour that she tutors.

Hence, the correct response is: C. The rate of change is 16. Georgia earns $16 per hour that she tutors.