From Longman Dictionary of Contemporary English(be on) a/the slippery slope(be on) a/the slippery slopeBritish English informalWORSE used to talk about a process or habit that is difficult to stop and which will develop into something extremely bad(be on) a/the slippery slope to/towards He is on the slippery slope to a life of crime. → slippery
Examples from the Corpus
slippery to/towards• In the 60s and 70s the announcement would have been the start of the slippery slope to election defeat.• He paused only to shake the wet from his shoulders, then trod up the slippery slope to the house door.• Too often we are faced with clamouring up the slippery slopes to the law more than sliding down them. 