Hello, my problem is I turn on the hot water and drips of water comes out. I don't think it is the faucet because the cold water works fine, plus I took off the hose that connected to the pipe and no water was came out. We have hot water everywhere in the house but the kitchen. Is there a busted pipe in my house or is there a simpler answer. Thank you!

If you have galvanized plumbing in the kitchen, then it is possible the nipple that the shut off is connected to is plugged with rust and scale.