The best thing for a slope is a variety of plantings with different root depths to hold the soil. http://houzz.com/photos/3566922

You could also terrace part of the slope, although that would be a more expensive option. http://houzz.com/photos/1295181

Drought tolerant plants are usually sun loving, but these can handle varying amounts of shade: Fire spike, wax myrtle, oakleaf hydrangea, sago Palm, wild petunias, variegated shell ginger, canna, and anemone

This is begging for you to divide it from the lawn by creating a large island bed beneath the trees. Where the grass stops growing well can be the general guide to the bed edge. In the beginning, I would define the bed edge and just mulch the entire bed. Later, when all weeds and grass are permanently eradicated from the bed (easiest way to kill with Round-up,) you can add groundcover. Also, prior to mulching, you could put down cardboard where there are weeds or grass and that would help smother and kill them (less Round-up.) Observe what is being used as groundcover for areas of similar size in Waco and choose what seems to do well and that you like the look of.

Prior to mulching, fix the places of erosion by adding topsoil and smoothing it out.

Thanks yardvaark. That's an idea I've been thinking of myself. I just have no idea how to design a bed with varying heights, textures, and colors to make it look good. I can grow some grass, but designing a garden isn't my thing.

Find out what kind of plants are recommended in your area for groundcovers in shade. Then take the picture above and mark out large area for three or four different groundcovers. Plant, mulch and keep the weeks out until they establish.

I wasn't thinking that a bed full of variety under trees is what will look good and be easy to maintain. A simple, single groundcover is what I had in mind.

Gotcha. Thanks. That sounds even better. What would you reccomend as a border to keep the Bermuda grass out?

I suggested three or four groundcovers because the area to be covered is VERY large. Too large, in my opinion, for just one groundcover; one groundcover for an area that large is like using a single species tree/shrub for a 100 ft. long privacy screen. Variety is needed for the health of the planting and for interest.

The erosion also has to be considered. Varied plantings are far more efficient at controlling erosion than a single ground cover. The trees are a great start, but in any areas where you can see the dirt is being washed away, you'll want plants of different heights and root depths.

blackdirt,

The whole idea behind erosion control, is to keep as much water off of that ground as possible. When it rains really hard, you need something to stop the stream, so, trees are usually your first line of defense. Then you would get something that will live under trees and be shorter, then another step shorter, and it goes on. Does that make sense? And roots are really important too, trees have wonderful roots, but you have to get something that will allow shrubs to grow around it too, then shrubs that will get tall and have wonderful strong roots, that is the second line of defense, then lower shrubs, then plants, and if you don't want a garden, ornamental grasses have roots that grow to haites, so they are awesome holding soil in place.

The picture of the front of your house on the side, you really need something done with that as soon as you can plant something there. That looks pretty bad, and will eventually start to erode the ground around your foundation.

I have to disagree that varied plantings somehow are all that much more magnificent at preventing erosion. Pretty much any groundcover that is healthy and growing well will prevent surface erosion. Also disagree that variety is needed. That's why there are some groundcovers that excel at large areas. Some are too rambunctious for small areas. If there was sunlight, turf could be that groundcover. Since there's not, a plant that tolerates shade is needed, but it doesn't need to be a complicated mix of things. Look at some of the Google images for groundcover and see that many cover expansive areas.