To represent the proportional relationships for Employee 1 and Employee 2, we use the formula for direct variation, which states that \( E = k \cdot h \), where \( E \) is earnings, \( h \) is hours worked, and \( k \) is the constant of proportionality (earnings per hour).
Employee 1
From the table provided for Employee 1, we can see:
- At 1 hour, the earnings are $10, so \( k = 10 \) (earnings per hour).
- Therefore, the equation for Employee 1 is: \[ E_1 = 10h \]
Employee 2
From the plotted points for Employee 2, we can derive the earnings per hour:
- From the coordinate points provided:
- At 1 hour, the earnings are $15.
- At 5 hours, the earnings are $75.
- This indicates a consistent rate of earnings per hour.
To find the constant of proportionality:
- Since the earnings and hours for Employee 2 shows that earning $75 corresponds to 5 hours, we can calculate: \[ k = \frac{E}{h} = \frac{75}{5} = 15 \]
- Therefore, the equation for Employee 2 is: \[ E_2 = 15h \]
Summary of the Equations
Thus, the equations representing the proportional relationships between earnings and hours worked for both employees are:
- For Employee 1: \[ E_1 = 10h \]
- For Employee 2: \[ E_2 = 15h \]