Open up a tarp and lay it on the floor under the cracked wall to protect it from damage.
Insert the tip of a flat-head screwdriver or a putty knife into the crack to widen it into a "V" shape. Once the shape is achieved, run the blade along the length of the crack again to remove the loose debris from it.
Plug in a vacuum and hold the hose up to the hairline crack. Vacuum out the crack thoroughly to suck out any remaining dust.
Open a tub of plaster patching compound if the wall consist of plaster, or open a tub of joint compound if it is drywall.
Insert a putty knife into the compound and scoop up approximately 2 to 3 tbsp. Place the knife at the bottom of the crack and angle it upward. Press the compound into the crack until you can no longer see it.
Scrape off any excess from the top of the wall by pulling the end of the putty knife along the wall.
Tear off a piece of fiberglass joint tape and place it in the wet compound directly over the location of the crack. Cover the tape with more compound until you cannot see it.
Wait for the compound to dry completely and sand it down with a medium-grit sandpaper until the repair is flush with the remainder of the wall.
Open a can of primer and apply it liberally to the repaired areas using a paint brush. Wait for the primer to dry and spot paint the repaired area to match the surrounding wall.