Answer: I think you are right, erosion will be a problem. It will also be difficult to spend much time working in the garden. Historically, gardeners and farmers living on hillsides have terraced them. You'd need to do some work, perhaps building some small retaining walls across the slope, then filling in behind them, to create flat areas for planting. If you think you'll be able to tend the garden, then you may be able to control erosion with some rows of perennial plants, mulching with hay, or growing a ground cover like Dutch white clover in the paths.
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