To determine Igor’s unit rate of change (i.e., his hourly wage), we need data on the hours worked each day and the corresponding amount he was paid. Since the values aren’t provided in your message, let's assume some hypothetical numbers to illustrate how to calculate the unit rate of change and graph the relationship.
Hypothetical Data
Let’s say Igor worked the following hours and received the following amounts:
- Day 1: Worked 4 hours, Paid $20
- Day 2: Worked 5 hours, Paid $25
- Day 3: Worked 6 hours, Paid $30
Calculating the Unit Rate
To find the unit rate (hourly wage), we can use the formula:
\[ \text{Unit Rate} = \frac{\text{Amount Paid}}{\text{Hours Worked}} \]
Using the data:
-
For Day 1: \[ \text{Unit Rate} = \frac{20}{4} = 5 \text{ dollars per hour} \]
-
For Day 2: \[ \text{Unit Rate} = \frac{25}{5} = 5 \text{ dollars per hour} \]
-
For Day 3: \[ \text{Unit Rate} = \frac{30}{6} = 5 \text{ dollars per hour} \]
Thus, Igor’s hourly wage is 5 dollars per hour.
Graphing the Relationship
To graph the proportional relationship:
-
Axes:
- X-axis (horizontal): Hours worked
- Y-axis (vertical): Amount paid in dollars
-
Plotting Points:
- For Day 1: (4, 20)
- For Day 2: (5, 25)
- For Day 3: (6, 30)
-
Drawing the Line:
- Since this is a proportional relationship (Igor earns the same amount per hour), the points will lie on a straight line that starts at the origin (0, 0).
- The slope of the line represents the unit rate, which in this case is 5 (rise over run).
The graph will look like this:
|
30 | ● (6,30)
|
25 | ● (5,25)
|
20 | ● (4,20)
|
15 |
|
10 |
|
5 |
|
0 |_____________________________
0 1 2 3 4 5 6 7
Hours Worked
Summary
- Unit rate: 5 dollars per hour
- Graph: A straight line passing through points (4, 20), (5, 25), and (6, 30), showing a linear relationship where the amount paid increases by $5 for every additional hour worked.