Solving Linear Equation by Guessing

Algebra Level 2

Given that f ( x ) = m x + b f(x) = mx+b such that f ( 2 ) = 0 f(2)=0 , f ( x 1 ) = f 1 f(x_1)=f_1 , and f ( x 2 ) = f 2 f(x_2)=f_2 . Find the value of f 1 x 2 − f 2 x 1 f 1 − f 2 . \frac{f_1x_2 - f_2x_1}{f_1-f_2}.

2 0 None of these choices 3

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Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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1 solution

Paul Ryan Longhas
Feb 19, 2015

( x 1 , f 1 ) = > f 1 = m x 1 + b (x_1,f_1) => f_1=mx_1+b ( x 2 , f 2 ) = > f 2 = m x 2 + b (x_2,f_2)=> f_2=mx_2+b ( 2 , 0 ) = > − b m = 2 (2,0) => \frac{-b}{m} = 2 So, x 2 ( m x 1 + b ) − x 1 ( m x 2 + b ) m x 1 + b − ( m x 2 + b ) \frac{x_2(mx_1+b) - x_1(mx_2+b)}{mx_1+b - ( mx_2+b)} = > b ( x 2 − x 1 ) m ( x 1 − x 2 ) => \frac{b(x_2-x_1)}{m(x_1-x_2)} = > − b m = 2 => \frac{-b}{m} = 2

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