You've probably had sufficient advice to be going on with already, but this extra tip won't hurt and will certainly help your slice. I have always had a natural fade in my ball flight. However, I have virtually eliminated it by placing the back foot further back at address, and slowing down the back swing so as to feel the body turning as the club goes back. I still generate a good deal of club head speed on the downswing, but with far more accuracy. I am hitting the ball much further too. A quick backswing can throw you off balance and is also much more difficult to control, usually causing an out-to-in swing path, e.g. slice.

Cheers.
Lee.