Question

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?

Employee 1 chart: Employee 1 Earnings per Hour Hours Earnings 1 10 2 20 3 30
Employee 2 graph earnings per hour: 15, 1. 45, 3. 75, 5
what would go in the 2 boxes below (1 point) The equation for Employee 1 is . The equation for Employee 2 is .

Answer 1

To find the equations for the proportional relationships for Employee 1 and Employee 2, we need to identify the constant of proportionality (or the rate of earnings per hour) for each employee.

### Employee 1

From the chart:
- For 1 hour, earnings = 10
- For 2 hours, earnings = 20
- For 3 hours, earnings = 30

We can observe that the earnings are directly proportional to the hours worked. The earnings per hour can be calculated as:

\[
\text{Earnings per hour} = \frac{\text{Earnings}}{\text{Hours}}
\]

Using any of the points:

1 hour: \( \frac{10}{1} = 10 \)
2 hours: \( \frac{20}{2} = 10 \)
3 hours: \( \frac{30}{3} = 10 \)

So, the constant of proportionality, or the earnings per hour for Employee 1, is 10.

Thus, the equation for Employee 1 is:
\[
E_1 = 10h
\]

where \( E_1 \) is the earnings and \( h \) is the hours worked.

### Employee 2

From the graph:
- For 1 hour, earnings = 15
- For 3 hours, earnings = 45
- For 5 hours, earnings = 75

Let's verify using one of the points:

1 hour: \( \frac{15}{1} = 15 \)
3 hours: \( \frac{45}{3} = 15 \)
5 hours: \( \frac{75}{5} = 15 \)

The constant of proportionality, or the earnings per hour for Employee 2, is 15.

Thus, the equation for Employee 2 is:
\[
E_2 = 15h
\]

where \( E_2 \) is the earnings and \( h \) is the hours worked.

### Final Answer

**The equation for Employee 1 is:** \( E_1 = 10h \)
**The equation for Employee 2 is:** \( E_2 = 15h \)