slackyoudaoicibaDictYouDict[slack 词源字典]
slack: [OE] In common with Dutch and Swedish slak, slack comes from a prehistoric Germanic *slakaz. This was derived from the same ultimate source that produced Latin laxus ‘loose’ (source of English lax, relax, release, and relish) and languēre ‘languish’ (source of English languish). The plural noun slacks was first used for ‘trousers’ in the early 19th century. (The noun slack ‘small pieces of coal’ [15] is a different word, probably borrowed from Middle Dutch slacke ‘waste produced by smelting metal’.)
=> languish, lax, relax, release, relinquish[slack etymology, slack origin, 英语词源]
slack (n.2)youdaoicibaDictYouDict
"coal dust," mid-15c., sleck, of uncertain origin, probably related to 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 (n.)).
slack (adj.)youdaoicibaDictYouDict
Old English slæc "remiss, lax, characterized by lack of energy, sluggish, indolent, languid; slow, gentle, easy," from Proto-Germanic *slakas (cognates: 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. 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.
slack (n.1)youdaoicibaDictYouDict
early 14c., "cessation" (of pain, grief, etc.), from slack (adj.). Meaning "a cessation of flow in a current or tide" is from 1756; that of "still stretch of a river" is from 1825. Meaning "loose part or end" (of a rope, sail, etc.) is from 1794; hence figurative senses in take up the slack (1930 figuratively) and slang cut (someone) some slack (1968). Meaning "quiet period, lull" is from 1851. Slacks "loose trousers" first recorded 1824, originally military.
slack (v.)youdaoicibaDictYouDict
1510s, "to moderate, make slack," back-formed from slack (adj.) after the original verb veered into the specialized sense of slake. Meaning "be remiss, inactive or idle, fail to exert oneself" is attested from 1540s; current use is probably a re-coining from c. 1904 (see slacker, and compare Old English slacful "lazy," sleacmodnes "laziness"). Related: Slacked; slacking.