If you're extending the current roof line down from the current fascia, this won't work if the roof is one story. As you extend the roof line it gets closer to the ground. By the time you get out 15 feet the roof will be hitting the ground. If the fascia is 10 feet off the ground and your roof pitch is 12 in 12, the roof will hit the ground in 10 feet.
If you want to extend the roof from the fascia board, the roof will be nearly flat going out 15 feet.
To get more slope, you would need to start the patio roof up onto the house.
In either case, the roof lines would not match.