Well I don't know about faster, but definitely more elegant. This expansion will cause all points to be five times further away from y=k. So, a point was d away from k, then after expansion it will be 5d away from k. So let's take the point they give us, (-3,2) goes to (-3,22).

Now since 2-->22 (ie. it increases), then 2>k. Otherwise 2-->a smaller number. So the distance from (-3,2) to y=k is 2-k. Likewise, the distance from (-3,22) to y=k is 22-k. This must be 5 times 2-k so:

22-k=5(2-k)

22-k=10-5k

4k=-12

k=-3