We keep a bucket under each sink to catch any leaks. Saturday we were getting something from under the kitchen sink when we noticed that the catch bucket was full. Uh-oh, we have a leak.
After some time, I was able to determine that the leak was coming from the hot water supply to the faucet. After several un-install and re-install of the hot water supply line to the faucet, I remained unsuccessful in stopping the leak. I decided I would go to Home Depot on Sunday morning and get a new supply line.
As planned, I went to Home Depot the next morning and got the new supply line. Thinking that the cold water side might leak soon as well, I bought two replacement lines. The hot water side was easily replaced. Not so with the cold water side ... I couldn't even screw the new line onto the valve outlet. When I reinstalled the old supply line I had taken off, it leaked. So now I was committed to replacing the cold supply line.
Further inspection showed that the valve outlet was tapered, unlike on the hot side. When I had replaced the faucet years ago, I had gone to Ace Hardware and just grabbed two faucet supply lines. It turned out that those were for tapered outlets. I bet there was an adapter on the cold side which I unwittingly discarded when I installed the then-new lines. The taper fit the cold side just fine, and I thought they fit the hot side. If I keep the line (with the taper) fairly straight at the valve outlet, the leak was negligible. And so it went that way for years.
This time I went to Home Depot and it seems they only sell the type that is flat and not tapered. The flat type fit the hot side perfectly, but could not be threaded onto the taper on the cold side. Another trip to Home Depot and their helpful plumbing specialist pointed me the solution I needed: an adapter. The adapter converts the taper to a flat, allowing me to use the same type of supply line on both the hot side and the cold side.
So the lessons are: (1) The valve outlets on the hot supply and cold supply under your sink may not be the same: one may be tapered and the other flat (they'll look different on close inspection). (2) There are different faucet supply lines sold; if it's for a tapered fitting, it will say so on the tag. (3) If you have a leak on one side and not the other, this may be the problem. A supply line for a taper will fit a flat, but will leak. A supply line for a flat will not fit a taper (it didn't for me). (4) If one of your valves have a tapered outlet, you can get an adapter to convert it to a flat.
(photo of faucet line is from the Home Depot website)