How can I correct it in an inexpensive way just to improve the visual appearance?
Hi Deni- Would landscaping it in a tier fasion work? Heres some examples that I have seen.
You might want to rethink filling in or leveling out. That slope may be there for drainage purposes. Before you decide, do your own recon, watch the yard the next few times that you have rain, see which way the yard drains. If you have no ponding or puddling or wash back to the foundation of your house, you could bring in some fill dirt to have it look more visually appealing.
One idea is to put larger/taller plants on the low side and shorter of the high side.
Get a truck load of top soil on low side, blend to center or all the way across packing it down firmly as u go along, dump couple bags of grass seed n water gently as directed on grass seed.