Drain for slop sink in basement

[Tom Tester]

I would like to add a slop sink to my basement. The first pic shows existing layout with Studor vent on top of a 1 1/2" vent, and rough in for shower/bathtub as well as bathroom sink drain rough in. the second pic shows the slop sink roughly on the place I want it with a wye just sitting on the cement at the bottom. My questions are:
1. Can I drain the slop sink into the 1 1/2" vent pipe in the lower back right corner roughly like the 2nd pic shows it leaning? The vertical pipe in the corner has the studor vent at the top and a cleanout at the top and the bottom? The length from the slop sink P-trap to the vertical vent in the corner is roughly 6'. I can get a 1/4" drop per foot on the horizontal 1 1/2" pipe, but is it legal to drain into ghat 1 1/2" vent? I am in Aurora, Co.

2. What is the total length allowed for horizontal 1 1/2" drain? If I have to go to the 2" drain closest to you in the 1st pic then the total length is probably 10'.
3. Do I have to tie into the 2" drain closest to you in the picture.
4. Any other suggestions from you professionals?
Edited to correct spelling and add a little clarity.

 

[Terry]

What you have is a bathroom group vented with an AAV vent. That should have been on the 2" and accessible for replacement and to allow air to it.
Laundry fixtures aren't allowed on the wet venting by code.
A 1.5" trap arm can go 42" to a vent.

 

[Sponsor]

 

[Tom Tester]

What you have is a bathroom group vented with an AAV vent. That should have been on the 2" and accessible for replacement and to allow air to it.
Laundry fixtures aren't allowed on the wet venting by code.
A 1.5" trap arm can go 42" to a vent.

Thank you for the response. I think I am ok on the AAV since all of the pipe in the first pic is 2" except the vertical 1 1/2" vent pipe coming up out of the cement in the corner, the lower 1 1/2" cleanout attached to that pipe, the vertical pipe attached to the top of that cleanout, and the lower connection on the wye where the upper horizontal 2" pipe connects to the side of the wye. So to restate it a different way, the wye has a 2" top where the AAV connects, a 2" side connection where the 2" horizontal vent pipe connects, and then a 1 1/2" bottom connection where the vertical vent pipe connects. The AAV will remain accessible from the water heater side of the plumbing even if I finish the bathroom side of that wall, and the AAV vent is 2" from the drain to the top of the AAV.
With all that said and considering the 42" restriction you mentioned, could I install another AAV behind the laundry tub since that room will never be finished and therefore the AAV will remain accessible? That would take care of the 42" restriction on the trap arm. Then if I understand you correctly, I cannot have that laundry tub drain into that 1 1/2" vent pipe in the corner. So if that is indeed the case can I just step my trap arm up to 2" and then connect that into the 2" vertical drain pipe for the sink using a wye?
Thanks again for your help!
Edit for clarity.