Venting washer and sink

I found this pic online, but it shows the two things I'm going back and forth with. Assume the leftmost pipe is the washer drain. Right now I just have that and the bottom pipe over to the right stack. I'm adding a sink between the two. My question is do I need the vent shown with the dotted black lines or just the center vent for the sink that goes over to the main vent? Hope that makes sense. Thanks for any help.