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Call lansdscape/hardscape architect...........

And you have no product posted or pictured.

Pictures of sideyard and backyard

Yes they will work on this type of slope...but if you are covering a large area it would be a good idea to grow a variation of ground covers..different heights...some flowering....mosses...st.johns wart for border areas where spreading to cover large areas and height are needed...research which covers like sun or shade and plant them in the best place for those conditions...start with planting spaced in small groupings so the ones that don’t thrive will be noticeable so they can be moved to better spots..this will also allow you to see how much each type spreads in those conditions...ground covers are an excellent alternative to grass..obviously...because they do not require any mowing...

Much too shady for thyme - that is a full sun plant. And a couple of other points....many groundcovers do not play well together. One will be more aggressive than another and will overwhelm the less vigorous one(s). And many groundcovers do not hold up well to much foot traffic, if that is a concern. And any number DO benefit from at least an annual mowing..........