on a slippery slope 情况越来越糟，急剧下滑

如果用 on a slippery slope 来形容某人或某事所处的状态，意思就是情况越来越糟，急剧下滑，如果不及时采取措施就会变得更糟 (有时也可以说 going downhill 滑坡) 。

例句

The country's economy was on a slippery slope following the closure of its biggest industry.

With his big drinking problem he was on a slippery slope to bad health.

请注意

如果某人被形容为 as slippery as an eel 意思就是此人奸诈狡猾，说明此人是靠不住的、不诚实的，而且很难捉住这个人的破绽。

I wouldn't recommend doing business with Bob; he's as slippery as an eel.