Is it possible to play ps2 games on a PS3 slim and if it is how do you do it?

No because Sony removed backwards compatibility from all PS3 models after 2007/2008!

There's a select few PS2 digital games on PSN that you can purchase and play but as far as PS2 disc games go, no you can't play em!

You can play PS1 games on all PS3 consoles however!

you can only play ps2 games that are downloaded from the psn store or on downloaded from a website with a jail broken ps3. The ps3 cannot play ps2 disc

*Only* those downloaded from the PS Store. It *cannot* play PS2 discs.