After dy - ";" is put by mistake, maybe, so remove it or adjust accordingly.

The algorithm actually steps along both axes simultaneously. The calculation of the increments ($X_{inc}$ and $Y_{inc}$) ensures that the coordinate along the dominant axis (the one with the larger $\Delta$) is guaranteed to change by exactly 1 unit (or $-1$) in each step, while the coordinate along the non-dominant axis changes by a fractional amount (the slope). The algorithm doesn't "step along" just the dominant axis; it increments both $x$ and $y$ in every single step.