[Catchmixer]

My kitchen sink drains very slowly.. I was adding a inline vent and it did not help.. I did snake drain over 25 ft. the backup is quick.. about 10 - 15 seconds, does the vent have to be higher than the sink or can I somehow vent under the sink.. thanks

[speedball1]

A few details and we start. Has your sink got a roof vent? If so, Have you snaked the roof vent yet?
You say you put out 25 feet of snake. Where did you snake from and what size is the snake? Did the sink always run slow od did this just start?
Does does the vent have to be higher than the sink or can I somehow vent under the sinkit back up and then drain right away or does it take some time?
Any gurgles or bubbles when it draiuns?

does the vent have to be higher than the sink or can I somehow vent under the sink

If you're asking about a AAV (Air Admittance Vent) the answer is No.
Here's a typical installation, (see image)

[Milo Dolezal]

If water backs up within 15 second than the blockage is either in the first San T or where pipe turns from vertical ( inside wall ) to horizontal ( below the floor ). See the attached drawing. Red marks show location of potential blockage. Snake it again with 3/8 snake. Use proper cutting knife tip.