The line with equation $y=2 x-6$ is reflected in the $y$-axis. What is the $x$-intercept of the resulting line?
(A) -12
(B) 6
(C) -6
(D) -3
(E) 0
Solution 1

To find the $x$-intercept of the original line, we set $y=0$ to obtain $0=2 x-6$ or $2 x=6$ and so $x=3$.

When the line is reflected in the $y$-axis, its $x$-intercept is reflected in the $y$-axis to become $x=-3$.

## Solution 2

When a line is reflected in the $y$-axis, its slope changes signs (that is, is multiplied by -1 ).

When a line is reflected in the $y$-axis, its $y$-intercept (which is on the $y$-axis) does not change. Thus, when the line with equation $y=2 x-6$ is reflected in the $y$-axis, the equation of the resulting line is $y=-2 x-6$.

To find the $x$-intercept of this line, we set $y=0$ to obtain $0=-2 x-6$ or $2 x=-6$ and so $x=-3$.

ANSwER: (D)