A contractor's total earnings from a job include a fixed amount plus an amount based on the number of hours worked. The values in the table represent the linear relationship between the number of hours worked and the contractor's total earnings in dollars.
Number of Hours Worked
Total Earnings
0
$20.00
5
$63.75
15
$151.25
25
$238.75
35
$326.25
40
$370.00
What is the rate of change of the contractor's total earnings in dollars with respect to the number of hours worked?
To find the rate of change, we need to determine the slope of the linear relationship between the number of hours worked and the total earnings.
Using the points (0, $20.00) and (40, $370.00), the slope can be calculated as:
Slope = (370 - 20) / (40 - 0)
Slope = 350 / 40
Slope = $8.75 per hour
Therefore, the rate of change of the contractor's total earnings in dollars with respect to the number of hours worked is $8.75 per hour.