Here in the Pittsburgh area a 5% slope is considered level. A 10% slope is just that a slope. Between the front of my porch and the back of the house is 47 feet and it drops 8 feet. There's a door in front and in back is a basement door and a garage door. That's a 17% slope. We get close to 40 inches of rain a year and we're 6 to 8 inches above normal in rainfall so far this year. There's been a lot of hillsides slide this year, but those are usually really steep hill sides, more like cliffs. I'd say that if your worried about runoff you bury a 4" pipe down the slope. With a 10% slope and a good stand of grass the grass should hold the ground.
If you're in LA, then I'd guess your real problem is you don't have rainfall to support a good stand of grass, but if you have a garden in this spot then just water the grass while you're watering the garden. With water and a half inch of
mushroom manure a year, or some other product, whichever you prefer, I think you'll be OK. But I don't know how wide your beds are which will block the rainfall runoff and channel it potentially into a narrow spot. If you have 8 foot wide raised beds and the original contours in between each pair of raised beds, then I think you'll be OK, with that good stand of grass.
If I'm wrong about my math I apologize profusely.