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.

(a) Determine y as a function of x.

(b) Graph this function in the window [0, 75000] by [0, 2000].

(c) Give an interpretation of the slope in applied terms.

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

(e) Determine graphically the income level at which the average itemized deductions are $1600.

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