Question

A contractor's total earnings from a job include a fixed amount plus an amount based on the number of hours worked.

Hours Worked - Total Earnings
0 - 20.00
5 - 63.75
15 - 151.25

The values in the table represent the linear relationship between the number of hours worked and the contractor's total earnings in dollars. What is the rate of change of the contractor's total earnings in dollars with respect to the number of hours worked?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of change of the contractor's total earnings with respect to the number of hours worked, we need to determine the slope of the linear relationship in the table.

Let (x1, y1) = (0, 20.00) and (x2, y2) = (5, 63.75) be two points on the line.

The slope of the line is given by the formula:
slope = (y2 - y1) / (x2 - x1)
slope = (63.75 - 20.00) / (5 - 0)
slope = 43.75 / 5
slope = 8.75

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. This means that for every additional hour worked, the contractor's total earnings increase by $8.75.