Amanda, do you have grass there that you are trying to maintain, or is this an area you want to plant with grass? How steep is the hill?
How do you know it's alkaline soil? That's pretty rare in GA.
Are you planning on mowing the steep hill?
Grass already exists but there are many bare spots. These were there when we moved in. In other areas of the yard, it is mostly weeds. The best I can speculate is that the yard was not properly maintained by the previous owners, and we're trying to fix this on a very tight budget. I used a test kit and found the soil in that and most other areas of my yard to be Ph 10 or higher.
Amanda, home pH test kits are notoriously inaccurate and it's highly unlikely your soil has a pH of 10. I'm in sand very near the beach and mine has a pH of 7.7 and that is high. I suggest you have a test done by the University of Georgia. You should indicate that you are trying to grow grass (specify the type if you know it) and they will tell you what you need to add. For all the how-to's, see this link:
I second Doug's remark: home soil test kits are rarely accurate. You don't have a pH of 10.
Bermudagrass might be your best bet.
Thanks for the input. I will get a more accurate Ph test done as soon as possible.