Use the table and image to answer the question.

Question

Employee 1
Earnings per Hour
Hours | Earnings
1 | 10
2 | 20
3 | 30
Employee 2 - Earnings per Hour
(5, 75), (3, 45), (1, 15), (0, 0)
The proportional relationship for the earnings and hours worked for Employee 1 is displayed in the table. The proportional relationship between the earnings and hours worked for Employee 2 is displayed in the graph. What is the equation that represents the proportional relationship between the earnings and hours worked for Employee 1 and Employee 2?
The equation for Employee 1 is __.
The equation for Employee 2 is __.

Answer 1

To determine the equations that represent the proportional relationships for both Employee 1 and Employee 2, we can analyze the data provided.

Employee 1

The earnings for Employee 1 are as follows:

• 1 hour: $10
• 2 hours: $20
• 3 hours: $30

These values indicate a consistent rate of earnings per hour. To find the equation, we can note that for every hour worked, the earnings increase by $10.

The equation for Employee 1 can be represented as: \[ E_1 = 10H \] where \( E_1 \) is the earnings and \( H \) is the number of hours worked.

Employee 2

The earnings for Employee 2 are given in the points:

• 0 hours: $0
• 1 hour: $15
• 3 hours: $45
• 5 hours: $75

From these points, we can see that the earnings also follow a consistent pattern. For instance:

• For 1 hour, earnings are $15, which implies a rate of $15 per hour.
• For 3 hours (3 hours x $15/hour), earnings are $45.
• For 5 hours (5 hours x $15/hour), earnings are $75.

Thus, the equation for Employee 2 can be represented as: \[ E_2 = 15H \] where \( E_2 \) is the earnings and \( H \) is the number of hours worked.

Summary

• The equation for Employee 1 is \( E_1 = 10H \).
• The equation for Employee 2 is \( E_2 = 15H \).