You want to hook in after
the sink ptrap and vent...
Here, you will want to cut into the pipe and add a 2" wye fitting to pick up the washing machine drain.
Install a 2" PTRAP at the washing machine, a mechanical vent (AAV
) and a standpipe about 30" tall if possible....see picture below. The AAV is required so that the washing machine PTRAP doesn't get siphoned when the kitchen sink/disposal/dishwasher drain past the connection for the new washing machine drain.
AAVS are sold at all home improvement stores...see picture. You will need an 1.5" threaded female adapter and some pipe dope to install the AAV into the PVC. This also suggests that you will need to reduce the 2" pipe using a 2"x1.5" PVC coupling
and then install an 1.5" STREET female adapter
for the AAV and you won't need to buy any 1.5" pipe...
I also included a 2" dandy cleanout
(also called a test tee) in the drain line. These are always a good idea... just in case. The cleanout at the PTRAP is a requirement where I come from.. in case something gets caught at the trap itself... although almost never happens with PVC.
Let me know if you have more questions...