I am considering putting a laundry room in my basement. The place where I want it is right next to the main vertical waste line. Could I T into this line and have the P-trap from the washing machine drain right into the main line? I'm not sure if I would run into venting issues. THANKS!

You may discharge your washer into the existing stack vent only if you vent it. I have put up a image of a AAV,(Air Admittance Valve) set up and the valve itself. I would suggest that you extend the raiser up to a few inches over the flood rim of the washer. Good luck, Tom