I added the waste pipe located at the front of the attached picture 1... The vertical arm on the left of the main waste pipe was already plumbed for future connection as was the vertical pipe on the right coming down from the second floor (you can see it in picture2).

Can anyone verify that this is correct (I haven't glued it yet). The vertical pipe from the second floor (on the right) connects to a 90 elbow that goes to a Y with cleanout. The 8' pipe is sloped about 4" - so I could clear the joist with the 45 and 90 at the left that goes to the sewer (picture 3).

Thanks in advance.

Where is it going? What is it for?

The new pipe will drain all the fixture in the 2nd floor bathroom (new addition) and connects directly to the sewer.

So far it looks OK. Falling fast but OK. Are you going to use purple primer? I noticed it was lacking on existing piping. I use support or j hooks or hangers every 4 feet