Option C — passing through the origin.
The equation $x - y = 0$ gives $y = x$. Substituting $(0, 0)$: $0 - 0 = 0$ ✓. So the line passes through the origin.
For $x - y = 0$, put $x = 0 \Rightarrow y = 0$, confirming it passes through $(0, 0)$. It is neither parallel to any axis (it has equal, non-zero slopes in both directions) nor does it pass through $(3, 2)$ since $3 - 2 \neq 0$. Examiners expect you to verify by substitution.