Scrape off the plaster from the damaged drywall joint, exposing as much of the underlying tape as you can. Get the knife under the tape so you can grasp it with your fingers. Pull it off slowly, taking the rest of the plaster off with it and completely exposing the drywall seam.
Spread joint compound over the seam from end to end, using a drywall knife. The compound line should be about 4 inches wide.
Press paper tape into the line of compound, covering it completely from end to end.
Spread compound over the tape from end to end. Press the front edge of the knife along the tape to squeeze the excess compound out from under it, embedding the tape fully. Allow the compound to set for four hours.
Spread a second coat of compound over the tape, making the line wider than it was by about an inch along each side. Make the new compound smooth and flat.
Let the compound set for four hours. Spread a third layer onto it, again widening the line. Let it set for 12 hours.
Use a drywall sander to sand the seam smooth. The wall is now ready for repainting.