Question

Igor’s summer job at the frozen yogurt shop paid him the following amounts in his first three days on the job (he got paid the same hourly rate every day).

Day 1 Day 2 Day 3
Hours worked 6 9 7
Amount paid $57.00 $85.50 $66.50


What is Igor's unit rate of change of dollars with respect to time; that is, how much is he paid for one hour worked?


Graph the proportional relationship described above, with the x-coordinate representing hours worked, and the y-coordinate representing amount paid in dollars.

Answer 1

9.5

Explanation:

I hope this helps!

Answer 2

`m = 9.5` -- Unit rate of change

See attachment for graph

Explanation:

Given

`\begin{array}{cccc}Hours & {6} & {9} & {7} \ \\ Amount & {57.00} & {85.50} & {66.50} \ \ \end{array}`

Solving (a): The unit rate of change.

This implies that we calculate the slope of the table.

This is calculated as:

`m = (y_2 - y_1)/(x_2 - x_1)`

Where:

`(x_1,y_1) = (6,57.00)`

`(x_2,y_2) = (9,85.50)`

`(x_3,y_3) = (7,66.50)`

The equation becomes

`m = (85.50 - 57.00)/(9 - 6)`

`m = (28.5)/(3)`

`m = 9.5`

To graph the table, we need to determine the equation.

To do this, we make use of:

`y = m(x - x_3) + y_3`

Substitute values for m, x3 and y3

`y = 9.5(x - 7) + 66.50`

Open bracket

`y = 9.5x - 66.50 + 66.50`

`y = 9.5x`

See attachment for graph