Derivative of the prhases "the skinny" and "forreal/true story", the term can flip-flop to be used at the beginning of a sentence, or to emphasize at the end of one's own, or another's story.
Rashad: Yo, on the slim, you've got to be one of the most beautiful girls I've ever met.
Jessica: Ooh, thank ya baby.
Jah: The whole club was buggin, kid. Straight buggin' out when Jay-Z came out last night...on the slim/
Quincy: On the slim?