slack (n.2) Look up slack at Dictionary.com
"coal dust," mid-15c., sleck, probably from Middle Dutch slacke, Middle Low German slecke "slag, small pieces left after coal is screened," perhaps related to slagge "splinter flying off metal when it is struck" (see slag).
slack (adj.) Look up slack at Dictionary.com
Old English slæc "loose, careless" (in reference to personal conduct), from Proto-Germanic *slakas (cf. Old Saxon slak, Old Norse slakr, Old High German slah "slack," Middle Dutch lac "fault, lack"), from PIE root *(s)leg- "to be slack" (see lax). Sense of "not tight" (in reference to things) is first recorded c.1300. Slack-key (1975) translates Hawaiian ki ho'alu First record of slack-jawed (1901) is in Kipling. Slack water "time when tide is not flowing" is from 1769.
slack (n.1) Look up slack at Dictionary.com
1794, "loose part or end" (of a rope, sail, etc.), from slack (adj.); hence figurative senses in take up the slack (1930) and slang cut (someone) some slack (1968). Meaning "quiet period, lull" is from 1851. Slacks "loose trousers" first recorded 1824, originally military.
slack (v.) Look up slack at Dictionary.com
Old English slacian "to loosen" (something), from the source of slack (adj.). Meaning "relax effort, weaken in trying" is from early 13c.; that of "to diminish in force" is early 14c. Related: Slacked; slacking.