Vent/Drain line

Can I run a bathroom 1 1/2" sink drain into a 2" drain line that also connects with a 2" bathtub drain that shares a 1 1/2" vent? The sink drain runs horizontal in the wall and turns down next to the tub so that I can run a vent up the wall at this location. Is this vent considered a wet vent?Please see attached drawing.

Thanks,
Tom

Yes that would be considered a wet vent. And you run the risk of the sink backing up into the tub, although that is unlikely (my opinion) with the 2" drain.

Would it be better if I ran the sink drain down to the 2" drain instead of running it horizontal first? Can I leave the vent where it is at and have it serve both the sink and tub? The sink is 3' 6" away from the vent and the tub is right next to the vent.