Compare Proportional Relationships Practice

Question

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1 of 51 of 5 Items
Question
Use the table and image to answer the 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)
The equation for Employee 1 is
.
The equation for Employee 2 is
.

Answer 1

To find the equations that represent the proportional relationships for Employee 1 and Employee 2, we can look at the data provided.

Employee 1:

From the table:

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

This indicates that each hour worked earns the same amount, so we can determine the unit rate.

To find the unit rate (the amount earned per hour), observe that:

• \( \text{Earnings} = 10 \times \text{Hours} \)

So, the proportional relationship can be expressed by the equation:

Equation for Employee 1: \[ E_1 = 10H \] where \( E_1 \) is the earnings for Employee 1 and \( H \) is the number of hours worked.

Employee 2:

From the graph:

• The points (0, 0), (1, 15), (3, 45), and (5, 75) suggest the following earnings for each hour:

For Employee 2, we notice that for every hour worked, the earnings increase by $15.

We can express this as:

• \( E_2 = 15H \)

where \( E_2 \) is the earnings for Employee 2.

Equation for Employee 2: \[ E_2 = 15H \] where \( E_2 \) is the earnings for Employee 2 and \( H \) is the number of hours worked.

Final Answer:

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