If you slow down at the end of a race, you slack off. When you use slack this way, it means to reduce your speed, to be sluggish, or to be negligent.
If something is loose, it's also said to be slack. A clothesline, for example, is slack if it is just hanging loosely between two trees. If you pull the clothesline tight, you reduce the slack. The root word of slack is the Old English word slæc, which means loose or careless. When you scold your friend for being careless about his responsibilities, you can say, "Pick up the slack!"