Answer: It might be very difficult to grow grass on a dry slope. And, if it's steep enough, it may be difficult to mow. Some options are tradional groundcovers, such as low-growing, mat-forming junipers or English ivy (Hedera helix), or a spreading perennial such as creeping phlox (Phlox subulata). Make sure whatever you select is very low growing to maintain the sightline if you need to be able to see out of, say, a driveway. If height is not an issue you might try a fast-spreading daylily. If you truly want lawn rather than groundcover, you might opt to have sod installed. It's established and an instant lawn. All you'll need to do is keep it watered.
Some shrubs to consider include Abelia x grandiflora 'Edward Goucher', Althea (Rose of Sharon), Azalea, Glenn Dale (Rhododendron hybrida), Scotch Broom, Euonymus (Winged Euonymus alata), Hawthorn, Holly, Juniper and Oakleaf hydrangea. There are dozens and dozens more so cruise your local garden center to find your favorites.
Best wishes with your new landscape!
Q&A Library Searching Tips