Problem 98

Solution 1:

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 $y = -3x + 6$.

The $x$-intercept of this new line is
found by setting $y = 0$ and solving
for $x$ which gives $0 = -3x + 6$ or $3x = 6$ or $x =
2$.

Solution 2:

The $x$-intercept of the original
line is found by setting $y = 0$ in
the equation of the line and solving for $x$, which gives $0 = 3x + 6$ or $3x = -6$ or $x
= -2$.

When the line is reflected in the $y$-axis, the $x$-intercept of the new line is the
reflection of the original line in the $y$-axis, and thus is $x = 2$.