Use the table and image to answer the question.

Question

Employee 1
Earnings per Hour
Hours Earnings
1 10
2 20
3 30
A line graph is titled as Employee 2, Earnings per Hour. The x-axis is labeled Hours ranging from 0 to 6 in increments of 1. The y-axis is labeled Earnings in dollars, ranging from 0 to 80 in increments of 5. A solid line joins four plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 15 right parenthesis, left parenthesis 3 comma 45 right parenthesis, and left parenthesis 5 comma 75 right parenthesis.

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?

(1 point)

Answer 1

To derive the equations representing the proportional relationships for both Employee 1 and Employee 2, we can analyze the information provided.

For Employee 1:

From the table given for Employee 1, we can calculate the earnings per hour:

• At 1 hour: Earnings = $10
• At 2 hours: Earnings = $20
• At 3 hours: Earnings = $30

The earnings increase by $10 for each additional hour worked, indicating a constant rate.

Thus, the relationship can be expressed as: \[ E_1 = 10H \] where \( E_1 \) is the earnings for Employee 1 and \( H \) is the number of hours worked.

For Employee 2:

For Employee 2, we analyze the plotted points from the graph:

• At 1 hour: Earnings = $15
• At 3 hours: Earnings = $45
• At 5 hours: Earnings = $75

We can observe that the earnings increase by $15 for each additional hour worked (from the point (0,0) to (1,15), and from (1,15) to (3,45), etc).

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

Summary of the Equations:

• For Employee 1: \[ E_1 = 10H \]

• For Employee 2: \[ E_2 = 15H \]

Therefore, the equations that represent the proportional relationships for both employees are:

1. Employee 1: \( E_1 = 10H \)
2. Employee 2: \( E_2 = 15H \)