Putting a deck roof on under the eve ?

I want to put a roof over my deck. I want to put it under the eve of my roof in the back and 4 post in the front. The deck is 8'x20'. I want to use fiberglass roofing that I want to be 9 to 10 ' over hang in the front. Can I put a 2x4 on the house under the eve to hold the roofing in place?. And frame the rest out to the post.

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