I wouldn't plant regular grass on the slope if it is really steep.
How are you going to mow it?
There are dwarf ornamental grasses, they really root in good, and daylilies really hold soil well.
With both, you are going to have to water it, even if you just set a sprinkler on it in the heat.
Have you considered a rock garden?
Mixed with the plants?
Could be quite attractive, look up online rock garden on steep slope and get some ideas,
Then you will never have to mow.