Rye grows fast, but it is not so good in the heat. Does best north of Wash DC or in the mountains. Hopefully, you are looking at bluegrass, which is slower, and it may be a low-growing compact dwarf type. There is probably some fine fescue in there as well. It may be you are really in tall fescue country. Shade, heat, dryness and humidity are tough on grass. Trees do fine. Members here who are closer to you can suggest locally adapted seed types. What is your fertility program? Slow release nitrogen during fall rains will be a help, I suspect.