My shower drain is draining very slow. I cleaned out the trap, I adjusted the drain plug assembly, I even took out the cleanouts in the main drain and ran a snake through it. But the drain is still slow. Could it be the vent, because it's the only thing I haven't checked yet. If it is the vent how do I remedy that?

Most shower clogs are caused by a build up of hair and grease. This will occur in the lateral drain line between the trap and the vent. Did you remove the strainer and snake from the drain? If not, then there's your problem. Send the snake,(with a auger tip), down the drain. You will hit the "J" bend of the trap about 6 or 8 inches down. Crank and work the snake around the bend. You now have a straight shot down the pipe. Put out 10 or 15 feet of snake and pull it back. Lot's of hair and crud on the auger tip?
To complete your job pour 2 large pans of boiling water down the drain. This will loosen up any crud remaining anhd flush it out into your mains. Put the strainer back and proceed to rub-a-dub in style. Cheers, Tom