Venting a new sink in basement

[sguntur]

Hi all, trying to finish my basement and have the following question (forgive the crappy drawing). I have existing plumbing rough-ins for a shower, toilet, and a sink. I would like to add a sink and/or washer marked in maroon (bottom right). The the green upward arrows are vents for the existing plumbing. Questions are:

1. Can I hook the sink/washer drain into the sewer line (4) coming in from the floor up above?
2. Can I vent the new sink/washer by connecting it (5) to existing vent (3) as shown by the dashed black line?

Any comments/suggestions welcome. Thanks!

 

[MicEd69]

1. Yes.
2. Yes, but. It probably doesn't matter much with your layout, but to be per code, the vent for the new sink needs to be vertical or no more than 45 degrees off vertical until it reaches 6" above the top of the flood level of the sink.