Question

One federal tax schedule states that if you are single and your taxable income is between $37,350 and $90,550, then you owe $5152.25 plus 25% of your taxable income over $37,350. Find a formula giving tax owed T as a linear function of taxable income I over $37,350. Both T and I are measured in dollars. (If an answer does not exist, enter DNE.)

Answer 1

The linear function is given by:

$T(i) = 0.25I - 4184.98 , 37350 \leq T \leq 90550$

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A linear function has the following format:

$y = mx + b$

In which

• m is the slope.
• b is the y-intercept.

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• Fixed taxes of $5152.52, thus:

$T = I + 5152.52$.

• The income over $37,350 is I - 37350.
• 25% of this is 0.25(I - 37350).

Thus, the linear function for the taxable income is given by:

$T(I) = 0.25(I - 37350) + 5152.52$

$T(I) = 0.25I - 9337.5  + 5152.52$

$T(i) = 0.25I - 4184.98 , 37350 \leq T \leq 90550$

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