If you find a stray cat hanging around your house, what should you do? First off, make sure the kitty is a stray. Some cats just like to wander and they have a permanent home somewhere else in your neighborhood. Give the cat a chance to go home.
If you determine that this cat has adopted your family, then you need to do some serious thinking about the responsibility. Just feeding it every once in a while isn’t doing the cat a favor, because you’ll create a dependency on your food that won’t be consistently met. If you feed a cat, you need to be prepared to do this permanently.
If this isn’t something you’re prepared to do, then you really shouldn’t start feeding the kitty. If no food is forthcoming, he’ll probably move along to a more receptive household. If you do end up feeding the cat, use good-quality dry food and provide fresh water as well.