When dragging a graphic line, any graphic lines that connect to that line (i.e. have an endpoint in the same place) should have that endpoint dragged too.
This is consistent with the behaviour of the line tool in drawing chained polylines, and would be helpful when editing things like PCB borders.
The lines are not stored in the PCB file as a chain of segments, but it should be "fairly" straightforward to support this by interating the list of all segments and checking endpoints.
The best outcome might be use of the point editor tool, like for zones, complete with "make corner" and "close", as well as the more advanced graphical editor, but this might be harder to do.
Side note: when done, the icon for the Line Tool should probably be the add_polygon icon (which is more like add polyline)
This is part of some geometry work along with lp:594060