Axis Translate
Modify > Translate > Axis Translate - Much like CAD tools, the “Axis...” tools work in a specific sequence. For Axis Translate, the sequence is that you pick where you want to move from to where you want to move to. There is no change in attitude for the object you have selected but you can use snapping again to provide more control.
The falloff modes for this tool are described in detail on the Modify page