Answer: Although ivy is inexpensive and spreads fast, I wouldn't recommend using it as a ground cover on your slope. It can be invasive and it will climb up the trunks of your trees unless you consistently keep it cut back. Instead of ivy, how about planting ajuga (carpet bugle) in the sunny spots and periwinkle (vinca minor) in the shady spots. Both are fast growing groundcovers and both are relatively well behaved. Other suggestions include pachysandra for the shade and blue rug juniper for the sun. Depending upon which plants you choose, the spacing will be a little different but as a general guideline, 6-12 inch centers for small plants will give you quick fill in; 8-12" if the plants are large. I would at least amend the planting holes with some organic matter to help the roots establish quickly and I would start at the top of the slope and work down so you're not accidentally sitting or standing on the new plants as you install them. You'll need to keep the new plants well watered until they get established (so I'd suggest planting in the fall so rains can help with the watering).
Your local garden center will probably have other groundcover choices. Best wishes with your landscape!
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