To assess the options you've given, let's break them down based on general knowledge about earnings trajectories for different professions:
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The plumber initially earns more money than the lawyer, but the lawyer earns more as more hours are worked.
- This can be true depending on the situation, such as if the plumber charges a high hourly rate while the lawyer is just starting out at a lower salary but increases their earnings significantly with experience.
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Bill Gates has the same y-intercept as the entry-level worker.
- This is unlikely unless we are comparing the earnings at a very specific point and context; typically, Bill Gates, as a billionaire, would have a much higher initial y-intercept (indicative of starting earnings) compared to an entry-level worker.
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The lawyer has a greater initial amount of earnings than the plumber.
- This scenario is also context-dependent. In many situations, lawyers tend to have a higher starting salary compared to plumbers, but this can vary based on geographic location and specific job market conditions.
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The plumber has a steeper rate of change than the entry-level worker.
- This might be true if the plumber’s hourly rate increases rapidly with experience, while the entry-level worker's salary increases at a slower rate.
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The entry-level worker has the same slope as the lawyer.
- This would typically not be true, as the salary progression path (slope) for a lawyer often differs from that of an entry-level worker in another field.
Based on these explanations, the likely applicable options are:
- The plumber initially earns more money than the lawyer, but the lawyer earns more as more hours are worked.
- The plumber has a steeper rate of change than the entry level worker.
So the options you might want to select are 1 and 4.