Here are selected entries from the 2010 tax table that show

Here are selected entries from the 2010 tax table that show the federal income tax owed by those married and filing jointly. The taxable income and the tax are both in dollars. Over what two parts of this table is the tax T a linear function of the taxable income t? Find formulas for both linear functions. (Let T be tax and t taxable income.) lower range T = 67500t upper range T = 68, 600

Solution

67500<= t <= 67900 : ( 67500 , 9291) and ( 67800, 9336)

slope = ( 9336 -9291)/300 = 45/300 = 0.15

T = mt +c ;

9336 = 0.15*67800 +c ; c = -834

T = 0.15t -834

68000 < = t <= 68600 ; ( 68000, 9369)and ( 68300, 9444)

slope = (9444 - 9369)/( 68300 - 68000) = 75/500 = 0.15

T = 0.15t +c ; 9444 = 0.15*68300 +c ; c = -801

T = 0.15t -801