How do I drag one end of a line?

When I select and move a line it drags the entire end, but I just want to drag the end point. Is there a way to do this? The line is connected to a face.

With nothing selected, hover the Move tool over the endpoint you want to move. When you see a green dot, click and drag. If the endpoint is constrained from moving in the direction you want by adjacent geometry, you can invoke Autofold by tapping Alt, thereby freeing the endpoint from constraint at the cost of an added face or two.