Can you recommend a hardy ground cover for a severely sloped area of my yard?

That type of growing location is usually very hot and dry because of all the reflected heat combined with the slope.

You might consider some of the following plants as ground cover: low mat-forming varieties of juniper, creeping thyme, lower-growing sedum varieties or creeping phlox.

If you don’t mind a slightly taller planting, you might consider the dwarf barberry, a mid-height juniper or perennials such as purple coneflowers, perovskia or artemisia.

No matter what you plant, however, you will need to prepare the soil by adding copious amounts of organic matter to it and then watering the new plants until they become established. Remember to water deeply but less often rather than a daily light sprinkling. Using several inches of organic mulch will also help reduce the watering need in addition to cutting down on the weeds while the plants are settling in.