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.
Best wishes with your new landscape!
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