Step in derivation of distance from line to point. Help needed I am working through < and have become stuck in a number of places, presently it is in turning step 10 into step 11 and the identity $$|ax_0+by_0+c|=|ax+by-ax_0-by_0|$$ I must be missing something from the previous steps. More help may be needed if and when I progress. Thanks.

WTS: $|ax_0+by_0+c|=|ax+by-ax_0-by_0|$

The thing to note is that $ax + by + c = 0$, as it's the line we're talking about. So we have that $|ax + by - ax_0 - by_0| = |ax + by + c - c - ax_0 - by_0| = |-ax_0 - by_0 - c| = |ax_0 + by_0 + c|$