Just for the heck if it, for a RHP, pitching to a RHB, stand on the right side of the rubber (your right as you stand with the rubber) and pitch a slider. Notice the bite of the ball. Now stand on the left side of the rubber and deliver the same pitch. See if you have the same bite on your slider to the RHB.
Now for a RHP, do the same exercise to a LHB, and take note of the movement.
It helps a lot if you have a video camera behind you, and about ten (10) feet high so the video is over your head.
In each case, your pitch will behave very differently to each batter.
Trust me on this one - you'll add a totally new dimension to a slider that'll be hard to figure out.