Answer: In some cases a steep slope is just not well suited to growing lawn grass; the heavy runoff makes seeding difficult and the slope also makes mowing dangerous. If the slope is that steep, you may need to consider terracing it or using a ground cover planting other than turf grass instead.
Or, if the slope is not so steep but the runoff is excessive in that area, you may need to consider changing the drainage in that part of the lawn to try to minimize the water running off at that part of the slope.
September is an ideal time of year to seed or sod the lawn, so you do have some time to do any needed grading and/or soil preparation. This should include first running some basic soil tests, adding organic matter and possibly fertilizer and/or lime as incated by the soil tests. Your local county extension can help you with the testing and interpreting the results and can also recommend specific grass varieties to try based on your soil type. They will also be able to help you develop a lawn establishment and maintenance plan based on your local conditions.
I would suggest you work with your local county extension to develop a plan for either reseeding or resodding the area, and/or consult with a professional with professional training and experience in grading to see if that can be adapted to facilitate growing lawn there.
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