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 Georgia's earnings for tutoring is the slope calculated from her earnings table, which is $16 per hour. This means that Georgia earns $16 for every hour of tutoring work she does. The correct option is C.

Step-by-step explanation:

To find the rate of change in the table showing the linear relationship between the number of hours worked by Georgia at the tutoring center, and the amount of money she earned, we can take two points from the table and calculate the slope of the line that represents this relationship. The slope, or rate of change, is determined by the change in the dependent variable (amount earned) divided by the change in the independent variable (number of hours worked).

Let's use the two points (3.2, $51.20) and (4.7, $75.20) to find the rate of change. Calculate the change in amount earned and the change in hours worked:

• Change in amount earned = $75.20 - $51.20 = $24
• Change in hours worked = 4.7 - 3.2 = 1.5 hours

Now, we calculate the rate of change (slope):

Rate of change = Change in amount earned / Change in hours worked

Rate of change = $24 / 1.5 hours

Rate of change = $16 per hour

This means that for each hour Georgia tutors, she earns $16. So, the correct option is C, which states that the rate of change is 16 and Georgia earns $16 per hour that she tutors.