What do I so with a large sloped drain in my front yard?

Check with the city to see what the options are, Many have restrictions to what you can do with their property. I am sure they also have suggestions for what they have seen others do around the drain.

Need a picture to visualize solutions.

Ivy? some other ground cover?

I agree w Mmorosko1...depends on daily sunlight or shade and plant zone. A large bed of liriope, pachysandra, creeping junipers (if it's full sun), dwarf azaleas (gumpo varieties), low spreading gardenias, even perennials & bulbs...a good nursery would be able to advise for your area. Keep it well mulched (3" deep) with a non-floating type...pine straw, shredded cypress, composted leaves, for example...some kinds will float downhill in hard rains. Or just well mulched & keep weeding occasionallY.

Ivy & vinca would work if it's in shade, but can creep into your grass or surrounding yards...you can mow it every couple of years once it gets established. If you're in a dry, water-scarce area rock w some plants, ornamental grasses, etc, might work, but I doubt that's the case if you have an established lawn..

I would make a dry creek bed out of this area, all you need is natural rocks and maybe a few perennial low growing plants and there you are!

dry river bed