Is it full sun? If so, you have many options. I happen to like moss phlox for full sun slopes. Also, you might like Geranium sanguineum.

Actually, now that I think about it -- for a slope, you would probably not want something herbaceous (non-evergreen) like Geranium. Instead, something like Bearberry or a creeping juniper might be better.

Thank you so much for answering. I feel like a non-evergreen would be prettier... is there a reason I would want an evergreen ground cover? Also, do they spread fast? Here is the picture of our yard. And again, thank you so much for your advice - I really appreciate it.

An evergreen would look nicer in winter (bare ground/dead stems and leaves vs. something green). It would also probably be a little better at holding the slope together and preventing erosion. Liriope or daylilies would also work there. Cotoneasters are nice. Check out the link below for more options.

Moss phlox is nice because it has attractive needle-like leaves that are evergreen and also flowers like crazy in Spring.

Another consideration is how well you can control an aggressive spreader if you decide to use one. If you have boundaries to keep spreading in check (looks like you do somewhat), you can really save money by getting something that is somewhat aggressive and will fill in quickly.

Here is a link that might be useful: Groundcovers