To determine the equations representing the proportional relationship between earnings and hours worked for Employee 1 and Employee 2, we need to clarify the details from the table for Employee 1 and the graph for Employee 2. Given that you mentioned a table and a graph but didn't provide specific data points or the slopes, I will explain how to derive the equations generally.
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Employee 1:
- If you have a table with hours worked (let's call them \(h_1\)) and corresponding earnings (let's call them \(e_1\)), you'd typically find the ratio of earnings to hours worked is constant. This ratio is the constant of proportionality (\(k\)).
- The equation would be in the form: \[ e_1 = k_1 \cdot h_1 \]
- To derive \(k_1\), take any pair from the table (for example: if 10 hours corresponds to $100 earnings, then \(k_1 = \frac{100}{10} = 10\)). The equation would then be: \[ e_1 = 10 \cdot h_1 \]
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Employee 2:
- For Employee 2, if you're given a graph where the slope represents the earnings per hour worked, the equation would similarly follow the proportional format. The slope (let's call it \(k_2\)) can be determined from two points on the graph.
- If the slope (or \(k_2\)) is found to be, for example, 15 (indicating $15 earned per hour), the equation would be: \[ e_2 = k_2 \cdot h_2 \]
- Thus, you would have: \[ e_2 = 15 \cdot h_2 \]
Final Answer:
- The equation for Employee 1 is \(e_1 = 10 \cdot h_1\).
- The equation for Employee 2 is \(e_2 = 15 \cdot h_2\).
(Note: Replace the \(k_1\) and \(k_2\) values with the actual constants derived from your data for Employees 1 and 2.)
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