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

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 y=

The equation for Employee 2 is y=

Answer 1

To determine the equations representing the proportional relationships between the earnings and hours worked for Employee 1 and Employee 2, we can analyze the given data for each employee.

Employee 1:

• From the table, we see the relationship is consistent:
  • 1 hour = $10
  • 2 hours = $20
  • 3 hours = $30

We can observe that for each hour worked, Employee 1 earns $10. Therefore, the earnings \( y \) can be expressed as:

\[ y = 10x \]

where \( x \) represents the number of hours worked.

Employee 2:

• From the graph, the plotted points are:
  • (0, 0)
  • (1, 15)
  • (3, 45)
  • (5, 75)

We can analyze the earnings:

• In 1 hour, Employee 2 earns $15.
• In 3 hours, Employee 2 earns $45.
• In 5 hours, Employee 2 earns $75.

We can deduce that for Employee 2, the earnings consist of an increment of $15 for each hour worked. Thus, the relationship is:

\[ y = 15x \]

where \( x \) is the number of hours worked.

Summary:

• The equation for Employee 1 is \( y = 10x \).
• The equation for Employee 2 is \( y = 15x \).