slat: [14] Slat was adapted from Old French esclat ‘piece broken off, splinter’. This was derived from the verb esclater ‘shatter’, a descendant of Vulgar Latin *esclatāre or *exclatāre. And this in turn may have been formed from a base *clatsuggestive of the sound of breaking. An alternative theory, however, is that it goes back to a prehistoric Germanic *slaitan ‘cause to split or break’, a variant of *slītan ‘split, break’ (from which English gets slice and slit).
The feminine form of Old French esclat was esclate, which has given English slate [14]. And its modern descendant éclat was borrowed by English in the 17th century in the metaphorical sense ‘brilliance’. It has been conjectured that esclater may have been related to Old French esclachier ‘break’, which could have had a variant form *esclaschier.
This would be a plausible candidate as a source for English slash [14]. => slate
slat (n.)
late 14c., earlier sclat (c. 1300), "a roofing slate, a thin, flat stone," from Old French esclat "split piece, chip, splinter" (Modern French éclat), back-formation from esclater "to break, splinter, burst," probably from Frankish *slaitan "to tear, slit" or some other Germanic source (compare Old High German slizan, Old English slitan; see slit (v.)). Meaning "long, thin, narrow piece of wood or metal" attested from 1764.