Question

Compare Proportional Relationships Practice
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Question
Use the table and image to answer the question.

This table shows the hourly earnings of Employee 1 along with the corresponding total earnings based on hours worked.
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 y=

The equation for Employee 2 is y=

Answer 1

To find the equations representing the proportional relationships for Employee 1 and Employee 2, we need to analyze the information given.

### Employee 1
From the table:

- When Hours = 1, Earnings = 10
- When Hours = 2, Earnings = 20
- When Hours = 3, Earnings = 30

We can see that the earnings increase by 10 for each additional hour worked. This indicates a constant rate where the earnings per hour is 10.

The proportional relationship can be expressed as:
\[ y = 10x \]
Where:
- \( y \) represents the Earnings
- \( x \) represents the Hours worked.

### Employee 2
From the line graph:

The plotted points show the following earnings for Employee 2:

- When Hours = 0, Earnings = 0
- When Hours = 1, Earnings = 15
- When Hours = 3, Earnings = 45
- When Hours = 5, Earnings = 75

We can observe that earnings increase by 15 for each hour worked. Thus, the earnings per hour for Employee 2 is 15.

The proportional relationship can be expressed as:
\[ y = 15x \]
Where:
- \( y \) represents the Earnings
- \( x \) represents the Hours worked.

### Final Answer
The equations for the proportional relationships are:
- The equation for Employee 1 is \( y = 10x \).
- The equation for Employee 2 is \( y = 15x \).