Although they aren't as much a fixture in backyards as they were decades ago, clotheslines allow cleaned and damp laundry to air dry in the sun. Doing so is a great energy saver, as the home or property owner won't have to expend any energy---thus dollars---on drying laundry in a dryer. Old clotheslines can sag over time, usually as a result of the soil shifting over the years. Luckily this is a DIY-type fix.
Remove the old line hanging between the clothesline poles using a pair of metal snips, which are strong enough to cut through the plastic sheathing and the metal wire underneath. Remove the line. In cases where the line may be rope-based, simply cut the rope with a knife. Completely remove all remnants of each type of line from the poles.
Use a point-end shovel to dig a perimeter around the base of one of the clothesline poles. Dig deep, down to the very end of the pole. Once it is loose in the soil, pull up to completely remove the pole from the ground (if you need help, get it.) Dig out any dirt in the hole and place a level vertically on the bottom of the hole to ensure the bottom is level.
Mix the quick drying cement as directed on the packaging. When ready, shovel the mix into the hole until it's about half full. Place the clothesline pole back into the hole and use the level horizontally across the top of the pole to ensure it is level. If so, fill the remainder of the hole with cement and hold the pole still for several minutes until the top of the cement solidifies. Repeat for the opposing clothesline pole.
Allow about a week of dry weather for the cement to cure underneath the surface. After a week or so, use steel wool to remove any rust on each pole if any is present. Paint the poles with a paint specifically formulated for metal and allow the paint to dry. String new wire or clothesline rope between the poles. Pull the line taut but not overly tight; you'll want a slight bit of give on the wire to accommodate for heavier laundry, like sheets, quilts or comforters.