To model Savannah's salary data with a linear function where \(x\) represents the number of years since 2000, we need to determine the correct linear equation from the given options.
From the table, we can first express the data:
- In 2000, \(x = 0\), the salary is 40000.
- In 2001, \(x = 1\), the salary is 42000.
- In 2002, \(x = 2\), the salary is 46000.
- In 2003, \(x = 3\), the salary is 44500.
Now, let's compute the slope \(m\) using any two points (for example, (0, 40000) and (2, 46000)): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{46000 - 40000}{2 - 0} = \frac{6000}{2} = 3000. \]
So our slope is approximately 3000 dollars per year.
Now, we can use the point-slope formula for a line, choosing the point (0, 40000): \[ y - 40000 = 3000(x - 0). \] This simplifies to: \[ y = 3000x + 40000. \]
None of the options provided match this equation directly, but we can explore the options listed:
- \(y = 39.625x + 4375\): This slope and intercept do not reflect our findings.
- \(y = 4375x + 39.625\): This matches the structure, but again does not reflect our findings.
- \(y = 1750x + 40500\): This slope is lower than the computed value and the intercept does not match.
- \(y = 40500x + 1750\): This has a non-matching slope and intercept as well.
Given that none of the provided options closely match our computed model, it seems there may have been an oversight in creating the options or there are errors in calculation or selection. However, we derived an effective linear equation based on the given data. In an ideal case, the best linear function is: \[ y = 3000x + 40000. \]
If pressed to identify among those options, we would require additional context or clarifications on the expected answers.
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