There are all kinds of great groundcovers for a shady spot under trees. The list of groundcovers that will thrive in your western Tennessee yard includes wild ginger (Asarum canadense), dwarf crested Iris (Iris cristata), Pachysandra (Pachysandra procumbens), foam flower (Tiarella cordifolia), and spiderwort (Tradescantia virginiana). You might also consider a couple of ferns, such as the cinnamon fern (Osmunda cinnamomea) or maidenhair fern (Adiantum pedatum). Some garden centers sell groundcovers in 50- or 72-plug trays, which is a good idea if you have a large area to cover. With the tree roots in the soil, it won't work to prepare the entire site. Just amend the soil in each planting hole as you go, stirring in a generous amount of compost. (Several trowels full is good.) Space the plants as close a 6 inches or as far as 18 inches, depending on how quickly you'd like them to cover the slope. Then, when you tuck each plant into the hole, create a little rim on the downward side of the slope that can catch and hold water.