To determine which graph represents the amount of money Max earns in \( x \) hours, we first need to calculate his earnings per hour.
Max earns $1,000 for an 8-hour shift. Therefore, his hourly rate can be calculated as follows:
\[ \text{Hourly Rate} = \frac{1000 \text{ dollars}}{8 \text{ hours}} = 125 \text{ dollars per hour} \]
Now, if \( x \) represents the number of hours he works, then the amount of money he earns can be represented by the function:
\[ \text{Earnings} = 125 \times x \]
Next, let's take a look at each of the points provided:
- Y: 9,900
- Z: 9,600
- W: 4,900
- X: 8,900
To determine how many hours correspond to each of these earnings:
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For Y (9,900): \[ x = \frac{9900}{125} = 79.2 \text{ hours} \]
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For Z (9,600): \[ x = \frac{9600}{125} = 76.8 \text{ hours} \]
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For W (4,900): \[ x = \frac{4900}{125} = 39.2 \text{ hours} \]
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For X (8,900): \[ x = \frac{8900}{125} = 71.2 \text{ hours} \]
Since all values calculated are based on Max earning $125 per hour, we need to find which point fits a linear relationship of earnings based on \( x \). The relationship is linear, and since he earns money as he works more hours, we are looking for the net multiplication of hours by his hourly rate.
Since Max has an hourly rate of $125, the amounts we computed do not clearly represent finite working hours or match the usual work hours.
Based on the values presented for \( Y, Z, W, \) and \( X \), although none are directly derived from the hourly calculation, if we are to choose based on a possible trajectory of earning compared to realistic work hours, W (4,900) represents a close, more realistic amount compared to typical hourly earning derived directly.
Thus the correct answer, based on reasoning through potential work hours aligning with typical shifts, would be:
C. W (as it closely aligns with more typical hours worked).
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