2015/16 AHSMC Part 1 Problem 3

Problem 3 of 16

The $x$ -intercept, $y$ -intercept, and slope of a certain straight line are three nonzero real numbers. The number of negative numbers among these three numbers is:

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Solution

The slope of the line with the $x$ -intercept at $(a,0)$ and $y$ -intercept at $(0,b)$ is $m = -\dfrac{b}{a}$ . If $a$ , $b$ are of the same sign, $m$ is negative and if they are of opposite sign $m$ is positive. Hence the number of negative numbers among $a$ , $b$ , $m$ is $1$ or $3$ . The answer is (E).

University of Alberta

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