A laser is fired at a flat mirror.

The laser beam starts at the point (0,5) following the equation y = 5 - x/3 heading down to the right.
The mirror follows the equation y=x/2.

Find the equation for the path the beam takes after it hits the mirror.

There's a nice geometric way of doing this with no trig, no vectors, or anything fancy.  The 45 degree angle was a pure coincidence, the method I have in mind doesn't require this either.