Hi Tyler ok sorry I didn't understand fully before about keeping the line at the same angle.

If I understand you correctly now, you can use the Transform > Move tool to do that if you set up a construction line to help get the snap point you need.

You'd start by putting the line onto one of those lines like this:



Select the line to move and run the Transform > Move command. Now you need to set up a construction line like this to help you get the snap you want:



The way you make a construction line is to press the mouse button down and keep it held down while you are dragging it. You want to snap the ends of the construction line onto the ends (or anywhere is ok) of the upper line that is being touched already. So you'll initially have the construction line going right over top of that line. Now you want to move that construction line over, you can do that by pressing and holding the mouse button down for 1 second or so on the little chevron that pops up, see here for more details:
http://moi3d.com/3.0/docs/moi_command_reference11.htm#constructionlines , on the menu that pops up after holding down the button there, choose "Relocate cline" and you'll be able to move the construction line to a different area while keeping it in the same orientation. This way you can basically capture a direction and apply it to a different spot.

After your construction line is relocated to the other end of the line being moved, you then want to use these 2 snap points for the Move command:



Hopefully that is what you needed? Please let me know if I still did not get it quite right though.

- Michael