Slippery Slope is not necessarily a logical fallacy if there is a logical connection between the beginning and end and a justification for it being reasonable.
For example, it is generally valid to look at any action the government takes in restricting the people in a slippery-slope manner because the government has a long and proven history of sliding straight down. "Don't worry, the seat belt laws are only a secondary offense," we knew it would eventually be a primary offense, and they there would eventually be roadblocks set up just to check for them. We were right.
There is a big "if" in your statement, namely, "there is a logical connection between the beginning and end and a justification for it being reasonable". So prove that compound statement and you do not have slippery slope otherwise, it is slippery slope and a fallacy.