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.

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MrRoyal MrRoyal · Answer 1 · 2021-02-08T02:14:05+01:00

Answer:

[tex]m = 9.5[/tex] -- Unit rate of change

See attachment for graph

Step-by-step explanation:

Given

[tex]\begin{array}{cccc}Hours & {6} & {9} & {7} \ \\ Amount & {57.00} & {85.50} & {66.50} \ \ \end{array}[/tex]

Solving (a): The unit rate of change.

This implies that we calculate the slope of the table.

This is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where:

[tex](x_1,y_1) = (6,57.00)[/tex]

[tex](x_2,y_2) = (9,85.50)[/tex]

[tex](x_3,y_3) = (7,66.50)[/tex]

The equation becomes

[tex]m = \frac{85.50 - 57.00}{9 - 6}[/tex]

[tex]m = \frac{28.5}{3}[/tex]

[tex]m = 9.5[/tex]

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

To do this, we make use of:

[tex]y = m(x - x_3) + y_3[/tex]

Substitute values for m, x3 and y3

[tex]y = 9.5(x - 7) + 66.50[/tex]

Open bracket

[tex]y = 9.5x - 66.50 + 66.50[/tex]

[tex]y = 9.5x[/tex]

See attachment for graph