The PS2 slim is backwards compatible, PS1 games and accessories such as the component cable everything ok..But I believe the original Fat PS2 is better for other purpouses such as hacking, and things of that nature... This.

Can you play PS1 games on a slim PS2?

All you have to do is insert the PS1 game inside the PS2 console (while still off), and then press the power button three (3) times in a row. This should allow the PS1 game to be played on the PS2 slim.

What model PS2 is backwards compatible?

You will be pleased to know that the PS2 is backwards compatible with most PS1 games. What is this? Note that I said 'most' there. Many of the titles that you know and love will work fine on both the Original PS2 model and the PS2 Slim.