Old English slæc "remiss, lax, characterized by lack of energy, sluggish, indolent, languid; slow, gentle, easy," from Proto-Germanic *slakas (source also of Old Saxon slak, Old Norse slakr, Old High German slah "slack," Middle Dutch lac "fault, lack"), from PIE root *sleg- "be slack, be languid."
Sense of "not tight" (in reference to things) is first recorded c. 1300. As an adverb from late 14c. Slack-key (1975) translates Hawaiian ki ho'alu. Slack water (n.) "time when tide is not flowing" is from 1769. Slack-handed "remiss" is from 1670s. Slack-baked "baked imperfectly, half-baked" is from 1823; figuratively from 1840.