To determine the equations that represent the proportional relationships between earnings and hours worked for Employee 1 and Employee 2, we can analyze the data provided.
Employee 1
From the table, we see the following data:
- For 1 hour → 10 dollars
- For 2 hours → 20 dollars
- For 3 hours → 30 dollars
The relationship here is linear and can be expressed with the formula: \[ \text{Earnings} = k \times \text{Hours} \] where \( k \) is the constant of proportionality.
To find \( k \): Using the first data point: \[ k = \frac{Earnings}{Hours} = \frac{10}{1} = 10 \]
Therefore, the equation for Employee 1 is: \[ \text{Earnings} = 10 \times \text{Hours} \]
Employee 2
From the graph, we have the following points for Employee 2:
- (0, 0)
- (1, 15)
- (3, 45)
- (5, 75)
To find the rate of change (slope) for Employee 2, we can again use the formula for \( k \): Using the point (1, 15): \[ k = \frac{Earnings}{Hours} = \frac{15}{1} = 15 \]
Thus, the equation for Employee 2 is: \[ \text{Earnings} = 15 \times \text{Hours} \]
Summary
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The equation for Employee 1 is: \[ \text{Earnings} = 10 \times \text{Hours} \]
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The equation for Employee 2 is: \[ \text{Earnings} = 15 \times \text{Hours} \]