PS3 Slim (all capacities) lacks native PS2 backward compatibility. The Emotion Engine + Graphics Synthesizer hardware was removed to cut cost, size, and power.
Select PS2 titles were re-released as **PS2 Classics** on PlayStation Store — recompiled/emulated downloads, not disc playback. ~50 titles released; program ended 2012.
Warning: Unofficial PS2 emulation on PS3 Slim (via CFW) is experimental, low compatibility, high instability. Not recommended.