Chapter 1.1, Problem 68E

Technology Exercises

Let $y$

denote the average amount claimed for itemized deductions on a tax return reporting $x$

dollars of income. According to Internal Revenue Service data, $y$

is a linear function of $x$. Moreover, in a recent year income tax returns reporting $\$20,000$

of income averaged $\$729$ in itemized deductions, while returns reporting $\$50,000$ averaged $\$1380$.

Determine $y$

as a function of $x$.

Graph this function in the window $\left[0,75000\right]$

by $\left[0,2000\right]$.

Give an interpretation of the slope in applied terms.

Determine graphically the average amount of itemized deductions on a return reporting $\$75,000$.

Determine graphically the income level at which the average itemized deductions are $\$1600$.

If the income level increases by $\$15,000$, by how much do the average itemized deductions increase?