Plumbing code requires to vent every plumbing fixture in your
house that contains a trap to keep your pipes from clogging and to protect your heath.
Without vents, negative pressure in the pipes can empty P-traps and
allow sewer gases into your home. Kitchen sink plumbing vent generally rise from kitchen sink drain line
to join a main vent stack that extends through the roof.
In case of the Kitchen sink plumbing is located within 5 feet of the waste stack we won't need to connect the kitchen sink drain line to the vent pipe as the drain pipe itself serves as the vent.

If your Kitchen sink is draining slowly and it isn’t due to a drain clog, it could be a sink vent issue. If the sink is connected to a roof vent it may be a good idea to consult a professional plumber. Either you will need to install an auto vent locally in your kitchen sink plumbing system or if you already have one it might needs to be replaced.