To determine which of the scenarios can be modeled by a linear function, we'll consider the characteristics of each scenario:
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The total pay of a person whose rate of pay per hour depends on the type of job.
- This scenario likely involves multiple different rates of pay based on job type, which does not create a linear relationship, as it changes depending on the job.
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The total pay of a person whose rate of pay per hour varies based on the difficulty of their job.
- Similar to the first scenario, the varying rates of pay based on difficulty suggest a non-linear relationship, depending on how the difficulty affects pay.
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The total pay of a person whose rate of pay per hour is fixed at $15 per hour.
- This scenario represents a linear function, as the total pay can be described by the equation \( \text{Total Pay} = 15 \times \text{Hours Worked} \). It produces a straight line when graphed.
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The total pay of a person whose rate of pay per hour varies depending on the number of hours worked per week.
- If the rate of pay changes based on the number of hours worked, such as overtime rates, this could indicate non-linearity. However, if consistent with standard hourly rates (e.g., with overtime calculated at a linear incremental rate), it may be modeled linearly under specific parameters.
Based on this analysis, the only unequivocal scenario that can be modeled by a linear function is option 3, where the pay rate is fixed at $15 per hour.