To find the equations representing the proportional relationships for Employee 1 and Employee 2, we need to analyze the information provided.
Employee 1
From the table, we have:
- When hours = 1, earnings = 10
- When hours = 2, earnings = 20
- When hours = 3, earnings = 30
As we can see, if we divide the earnings by the hours, we find that:
- \( \frac{10}{1} = 10 \)
- \( \frac{20}{2} = 10 \)
- \( \frac{30}{3} = 10 \)
Since the ratio is constant (10), we can write the equation for Employee 1 as follows: \[ E_1 = 10H \] Where \( E_1 \) represents the earnings of Employee 1 and \( H \) represents the hours worked.
Employee 2
From the graph, we observe the following points:
- Coordinates: (0, 0), (1, 15), (3, 45), (5, 75)
We can calculate the rate of earnings per hour for Employee 2:
- For 1 hour, earnings = 15
- For 3 hours, earnings = 45
- For 5 hours, earnings = 75
If we divide the earnings by the hours:
- \( \frac{15}{1} = 15 \)
- \( \frac{45}{3} = 15 \)
- \( \frac{75}{5} = 15 \)
Again, since the ratio is constant (15), we can write the equation for Employee 2 as: \[ E_2 = 15H \] Where \( E_2 \) represents the earnings of Employee 2.
Summary of the Equations:
- For Employee 1: \[ E_1 = 10H \]
- For Employee 2: \[ E_2 = 15H \]
These equations represent the proportional relationships between earnings and hours worked for both employees.