My business pays tax on income, and the tax paid is a linear function of income.If my income is $10420 then the tax owed is $929.60.If my income is $11309 then the tax owed is $1000.72.How much tax do I owe if my income is $11874?

Question

My business pays tax on income, and the tax paid is a linear function of income.If my income is $10420 then the tax owed is $929.60.If my income is $11309 then the tax owed is $1000.72.How much tax do I owe if my income is $11874? ​

Quizplus · Accepted Answer

The tax function can be represented as T(x) = mx + b, where T(x) is the tax owed, x is the income, m is the slope of the line, and b is the y-intercept. To find m, use the two given points: (10420, 929.60) and (11309, 1000.72). The slope m = (1000.72 - 929.60) / (11309 - 10420) = 71.12 / 889 = 0.08. To find b, substitute one of the points into the equation: 929.60 = 0.08(10420) + b, solving for b gives b = 929.60 - 833.60 = 96. Using the equation T(x) = 0.08x + 96, for x = 11874, T(11874) = 0.08(11874) + 96 = 950.92 + 96 = 1045.92.

My Business Pays Tax on Income, and the Tax Paid