Question

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 What is the rate of change of the contractor's total earnings in dollars with respect to the number of hours worked?

Answer 1

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Answer 2

To find the rate of change of the contractor's total earnings with respect to the number of hours worked, we look at the slope of the linear relationship between the two variables. The slope represents the rate at which the total earnings change for each additional hour worked.

From the table, we can see that the total earnings increase by $50 for every additional hour worked. Therefore, the rate of change of the contractor's total earnings with respect to the number of hours worked is $50 per hour.

Answer 3

Let's calculate the rate of change by finding the slope of the linear relationship between the total earnings and the number of hours worked using the values from the table.

We can choose two points from the table to calculate the rate of change. Let's choose the points (0, $100) and (6, $250), where 0 represents the initial hours worked and 6 represents the additional hours worked.

Slope = (Change in total earnings) / (Change in hours worked)
Slope = ($250 - $100) / (6 - 0)
Slope = $150 / 6
Slope = $25

Therefore, the rate of change of the contractor's total earnings with respect to the number of hours worked is $25 per hour.