toilets
 

I'm instaling a toilet on the first floor the toilet sits 4' to the left of the toilet in the basement I would like to tap into the pipe line in the basement. There's also a drain line in this area from the kitchen sink can I use this as my vent?????????

If it turns out that you can't, then see if you can use an air admittance valve as a vent instead. They're commonly used in kitchen "islands" where you might have a sink, but don't want a vent pipe sticking out of the island and going up to the ceiling.

How To Install Air Admittance Valves: Diy Hints, Tips & Advice : Diy Doctor

The only way we could give you an accurate answer is to have you provide a sketch of your existing piping and include what you propose to add.

Unfortunately proper venting is not as simple as adding aav's and calling it done.
There are often ramifications to adding a flow of water to a pipe that can upset the venting of other fixtures.