You have a few options, depending on your budget and your energy.
1. Add a retaining wall (most expensive option). If you place it towards the bottom of the slope and make it a couple of feet high, you can then fill in behind it to lessen the slope. You can then plant on top of the retaining wall/in front of the fence, which will soften the fence.
2. Forget about grass...you will never be happy. Add a sun loving groundcover, like Ajuga. You can add other plants too, but I would just keep it simple. If you like, along with the Ajuga, add tall ornamental grasses in front of the fence, such as Maiden Grass...or mix Maiden Grass and Zebra Grass.
3. Re-grade by adding more soil. If you extend the hill onto your flat lawn area, the slope will be lessened. This, however, will take away from your level lawn area.
Whatever you decide, add lots of topsoil because the earth there looks very rocky and poor.
