This is probably as basic as it gets, but I'm a newish homeowner contemplating a bathroom renovation (complete, to the studs and joists) and am trying to get a little better understanding of what it will entail.

Specifically, if two fixtures (tub and vanity sink) drain into the same horizontal pipe that runs to the soil stack, where in that pipe should the vent "riser" (?) begin? Does one vertical pipe installed down the line from both tub and sink adequately serve as a vent? Or does there need to be a second vent pipe between the two fixtures?

The sink is about 3 feet from the stack, and the tub drain only about 7 or 8 (very small bathroom). They have both drained very slowly since we moved in but I assume that is due to cruddy old pipes more than inadequate venting, but after the redo I'd like proper drainage (no more standing in inches of water while showering would be a good thing).