If someone or something is on a slippery slope, it's in a situation which is getting worse and will continue to get much worse. Sometimes we say it's 'going downhill'.
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.
If someone is described as being as slippery as an eel, it means they are not honest and you can't trust them. It is difficult to catch them behaving in this way.
I wouldn't recommend doing business with Bob; he's as slippery as an eel.
This photo shows skier Tina Weirather of Liechtenstein. She has won her first World Cup victory after descending down a steep and fast course to win a super-G (a super giant slalom) race in Garmisch-Partenkirchen in Germany.