Answer: Bare soil on a slope is always at risk of severe erosion. You need to cover the soil surface as soon as possible.
You could use burlap pegged down to cover the bare ground, then cut slits in the burlap to plant through. Then mulch over top of the burlap. Groundcover shrubs such as junipers will help hold the soil, as will the mulch. An organic mulch is better for your plantings than stone mulch. Stone mulch reflects heat and stresses the plants as a result, it also does not break down over time to feed the soil.
If the soil has washed away in large quantities, you should look at the drainage pattern for the property and see if it needs to be adjusted. This is important because severe erosion can undermine retaining walls and possibly the overall slope. I would strongly suggest you consult on site with a a professionally trained, degreed landscape architect or other professional with experience in drainage issues. Best of luck with your new home!
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