Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.7 Junior Find the answer

The line with equation $y=3x+6$ is reflected in the $y$ -axis. What is the $x$ -intercept of the new line?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

When a line is reflected in the $y$ -axis, its $y$ -intercept does not change (since it is on the line of reflection) and its slope is multiplied by -1 . Therefore, the new line has slope -3 and $y$ -intercept 6 , which means that its equation is $y=-3 x+6$ . The $x$ -intercept of this new line is found by setting $y=0$ and solving for $x$ which gives $0=-3 x+6$ or $3 x=6$ or $x=2$ .

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