Pergola roof diy planning

[Max T.]

Planning to put a toja grid pergola on my deck when the weather gets warmer. It will measure about 10 feet long (from the back of the house) by about 12 feet wide (width of the deck).

I want to put a corrugated metal roof on it. I plan on using joist hangers with 2x4s every 16 inch on center.

The water will run off the side (the 12 foot width). What should my minimum pitch be? How much higher should the high side be compared to the low side, considering a 12 ft run?

We do get some snow in Philly. Not a ton but more than a little bit. Heat cable to melt it after bigger storms?