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.The rate of change is 8. Georgia earns $8 per hour that she tutors.
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Answer 1

To find the rate of change (slope) of Georgia's earnings per hour, we can use the data provided to calculate the earnings per hour based on the pairs of hours worked and corresponding earnings.

We can choose any two points to calculate the slope:

1. For \(x = 3.2\) hours and \(y = 51.20\) dollars
2. For \(x = 4.7\) hours and \(y = 75.20\) dollars

Calculating the Rate of Change:

The formula for the slope \(m\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's use the first two points:

• \(y_1 = 51.20\), \(x_1 = 3.2\)
• \(y_2 = 75.20\), \(x_2 = 4.7\)

Now substitute into the formula:

\[ m = \frac{75.20 - 51.20}{4.7 - 3.2} = \frac{24}{1.5} = 16 \]

This means the rate of change is 16.

Thus, the interpretation of this rate of change is: Georgia earns $16 for each hour she tutors.

Therefore, the correct response is:

C The rate of change is 16. Georgia earns $16 per hour that she tutors.