New Outdoor deck Roof

Hi trying to help the old man out and build a pergola over his existing deck, and cover it with corr iron. Im a bit stuck for ideas as the ranch slider from the house to the deck is quiet close to the eave/facia/spouting and am worried that the roof will be too low. I have attached a pic, I had an idea of taking off some roofing of the house's existing roof and try and bolt some posts to the existing rafters, then have a bearer and rafters for the new pergola roof running off that going...

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