How to move location of entire line renderer, not each point

I have a line renderer that draws a coil with several loops. When a button is pressed I want the coil to move and rotate, although since each position of the line is scripted as a 3d coordinate the line always stays in the position of those scripted coordinates, even if I change the transform values in the Inspector.

The coil has too many coordinates to re-render in the Update() function every frame. Is there another way to move the entire line-renderer in relation to the scene?