Problem 377

Solution 1

To find the $x$-intercept of the original line, we set $y=0$ to obtain $0 = 2x - 6$ or $2x = 6$ 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 $y=2x-6$ is reflected in the $y$-axis, the equation of the resulting line is $y = -2x - 6$.

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