Ask Mr. Smarty Plants

You did not say what the sun exposure on the slope is, and that can be important in selecting plants for an area. However, we can give you several suggestions and by following the plant links to the individual pages on those plants, you will find out how much sun they need, moisture, growing conditions and so forth.

Native grasses, adapted to your climate and rainfall, are always the best choice for erosion control. They have long fibrous roots that will grab the soil and hold it. These are not lawn grasses, that are mowed every week, but prairie grasses, which can be cut down to about 6" every Spring.

We will go to our Recommended Species section, select North Central Texas from the map, and then select on "grass and grass-like plants" under General Appearance. We will check with the USDA  Plant Profiles in each grass we select to make sure it grows in Tarrant and Johnson Counties, so the climate, soils and rainfall should be acceptable for those grasses. Native American Seed has an excellent article on Planting Tips for Native Grasses. You should also check out their catalog for grass mixes that might work in your situation, such as Thunder Turf (for sun), Blackland Prairie Mix (also full sun) or Shade-Friendly Grass Mixes. Mixes tend to be more satisfactory because of the diversity, allowing the area to nearly always have some plants that are attractive. 

You will notice that the article on native grasses we referred you to recommends planting grass seed in the Spring, because that is when the seeds germinate anyway. Depending on how steep your slope is, you may need to use an erosion control blanket. If you sprinkle grass seed on a hillside in the Spring, the first rain is going to wash it all down to the bottom of the slope, possibly on someone else's property, who isn't thrilled with that. There are a number of brands and types of these blankets that should be available at large home improvement and garden stores, with instructions for their use.

Grasses for erosion control in Burleson TX:

Poa arachnifera (Texas bluegrass)

Schizachyrium scoparium (little bluestem)

Sorghastrum nutans (Indiangrass)

From the Native Plant Image Gallery:

Muhlenbergia lindheimeri

Poa arachnifera

Schizachyrium scoparium

Sorghastrum nutans