No other drains in the house are slow or backing up, but my kitchen sink fills and won't drain properly. We've run a 25ft snake down the pipe from inside the house (under the sink at arrow) and from the air vent on the roof, but haven't found any clogs. When my husband took off the cap (at arrow) under the sink, he could see water flowing freely through the opening when he turned on the faucet. It only takes two (electric) kettle fulls of water to have water backed up into the sink, though. I only mentioned electric kettle to relate its size and the amount of water it takes to back up the sink again. It takes more than an hour to drain completely when there's about 3-4 inches of water in each side of the sink. We have used a couple of different drain cleaners over the last few days trying to clear the blockage, but nothing is working so far.
I hope these added details help clarify any questions.