Adding a utility sink in my Garage

Thanks in advance for your help with this!!!

I am planning to add a utility sink into my garage. I have access to a 3" drain line that comes from the upstairs master suite tub, shower and two sinks (toilet has a dedicated drain line).

My plan is to place a wye in the 3" drain line, com out of the wall at a 90 and then on to the p trap for the sink. In that Line from the 90 to the p trap I plan to install a T and send off and vent with a Studor vent.

Will this work I expected? Any comments would be greatly appreciated.

Thanks!

Slope all drain lines 1/4" per linear foot toward the main drain line.
Check with your Building Inspection Department to see if air admittance valves (aka Studor vents) are allowed by local code.
Good luck!
Mike