what is the best way to extend or retract an existing line to an intersect point?
Grab the end with the Move tool and move it.
but that does not keep the other end anchored, does it?
If there is an intersection, the edge should be broken there and you can simply erase the extra part. To extend an edge you can use the line tool. Click at the starting point and then hover over the existing edge until you see an “on edge” inference. Press and hold shift while you extend the edge.
Or use the move tool as @DaveR suggested, again using inference as needed. If you click the move tool on the end of the edge, it will move that vertex while leaving the other end in place.
thank you. that worked.