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Question
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.

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

The rate of change in the linear relationship between the number of hours worked and the amount earned is $16 per hour. This means Georgia earns $16 for each hour she works at the tutoring center. Option C is the correct answer.

Step-by-step explanation:

The student is asking about the rate of change in a linear relationship, which represents the amount of money Georgia earns per hour worked at the tutoring center. The rate of change can be calculated by looking at the change in the amount of money earned for an equivalent change in the number of hours worked. To find the rate, we select two points from the table and divide the difference in Georgia's earnings by the difference in the number of hours worked.

For example, using the points (3.2, $51.20) and (4.7, $75.20), we calculate the rate of change as follows:

Rate of change = (Amount Earned at 4.7 hours - Amount Earned at 3.2 hours) / (4.7 hours - 3.2 hours)

Rate of change = ($75.20 - $51.20) / (4.7 - 3.2)

Rate of change = $24.00 / 1.5 hours

Rate of change = $16 per hour

Therefore, the correct option is Option C: The rate of change is 16, meaning Georgia earns $16 per hour that she tutors.