What is the correct slope for a deck, and why?
I’d use 1/8” per foot slope because 1) it’s enough to actually allow water to run off, and 2) the deck will “appear” flat

You don’t want standing water on your deck. It can cause rot, etc. I live where we get a ton of rain. It’s important to get rid of water on wood, etc. on the exterior of a home.

When you look at the deck, it will appear flat AND your soup bowl will not spill when you place it on a table.