Google Classroom

Microsoft Teams
Problem
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

Day

Day

Hours worked



Amount paid



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?
The unit rate is
dollars per hour.
Graph the proportional relationship described above, with the

-coordinate representing hours worked, and the

-coordinate representing amount paid in dollars.



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1 answer

To find Igor's unit rate of change in dollars with respect to time (i.e., how much he is paid for one hour worked), we will first need the total hours worked over the three days as well as the total amount paid.

Let's assume you have the following information for Igor's first three days:

  1. Day 1

    • Hours worked: \( h_1 \)
    • Amount paid: \( p_1 \)
  2. Day 2

    • Hours worked: \( h_2 \)
    • Amount paid: \( p_2 \)
  3. Day 3

    • Hours worked: \( h_3 \)
    • Amount paid: \( p_3 \)

Step 1: Calculate the total hours worked and the total amount paid

You can calculate:

  • Total hours worked: \( H = h_1 + h_2 + h_3 \)
  • Total amount paid: \( P = p_1 + p_2 + p_3 \)

Step 2: Calculate the unit rate

To find the unit rate of change (dollars per hour), use the formula:

\[ \text{Unit rate} = \frac{P}{H} \]

This gives you the amount Igor earns for one hour of work.

Step 3: Graph the proportional relationship

To graph the relationship:

  • Use a cartesian coordinate system.
  • On the x-axis (horizontal), represent the hours worked.
  • On the y-axis (vertical), represent the amount paid in dollars.
  • Plot the points for each day:
  1. For Day 1, plot the point \( (h_1, p_1) \).
  2. For Day 2, plot the point \( (h_2, p_2) \).
  3. For Day 3, plot the point \( (h_3, p_3) \).

Draw the line

Since it is a proportional relationship, the points will lie on a straight line, passing through the origin (0,0). The slope of the line will represent Igor's unit rate of pay in dollars per hour.

Conclusion

To complete the problem, you’ll need the specific values for the hours worked and amounts paid from your data, allowing you to calculate the unit rate and create the graph based on that information. If you can provide those values, I can help you calculate or validate the unit rate and describe the graph further!