2016/17 AHSMC Part 1 Problem 6

Problem 6 of 16

Two straight lines with nonzero $x$ and $y$ -intercepts have the following property: the $x$ -intercept of the first line equals the $y$ -intercept of the second line, and the $x$ -intercept of the second line equals the $y$ -intercept of the first line. If the slope of the first line is $m$ , then the slope of the second line is

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Solution

It is given that if $(a,0)$ and $(0,b)$ lie on the first line then $(0,a)$ and $(b,0)$ lie on the second line. The slopes of the lines are then $m = -b/a$ and $-a/b = 1/m$ , respectively. The answer is (C).

University of Alberta

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