To find the equations that represent the proportional relationships between earnings and hours worked for Employee 1 and Employee 2, we can analyze each case separately.
For Employee 1:
The data provided for Employee 1 shows a linear relationship between hours worked and earnings:
- If 1 hour worked = $10 → \(1 \times 10 = 10\)
- If 2 hours worked = $20 → \(2 \times 10 = 20\)
- If 3 hours worked = $30 → \(3 \times 10 = 30\)
From this analysis, we see that for every hour worked, Employee 1 earns $10. Therefore, the equation representing the relationship between hours (h) and earnings (E) for Employee 1 can be expressed as:
\[ E_1 = 10h \]
For Employee 2:
The coordinates from the graph for Employee 2 are:
- (0, 0)
- (1, 15)
- (3, 45)
- (5, 75)
To find the relationship, we can observe the change in earnings per hour:
- Between 0 and 1 hour: Earnings increase from $0 to $15 → This means they earn $15 for the first hour.
- Between 1 and 3 hours: Earnings increase from $15 to $45 → This means they earn $15 per additional hour.
- Between 3 and 5 hours: Earnings increase from $45 to $75 → This means they earn $15 per additional hour.
Thus, Employee 2 earns $15 per hour as well. The equation representing the relationship between hours (h) and earnings (E) for Employee 2 is:
\[ E_2 = 15h \]
Summary of Equations:
- Employee 1: \( E_1 = 10h \)
- Employee 2: \( E_2 = 15h \)
These equations describe the proportional earnings based on hours worked for both employees.
1 answer