A second hyperplane

Increasing $b$ raises every score by the same amount, so it slides the boundary without rotating it. The first point to flip is the one with the smallest positive score.

Boundary. $x_1 + 3x_2 - 6 = 0$, i.e. $x_2 = 2 - x_1/3$.

Norm. $\lVert\vec{w}\rVert = \sqrt{1 + 9} = \sqrt{10} = 3.1623$.

Which flips first. Decreasing $b$ lowers every score equally. $P$ and $R$ tie at $+3$, so both flip together at $b = -9$. Going the other way, increasing $b$ raises scores: $S$ at $-5$ flips before $Q$ at $-6$, at $b = -1$.

What that shows. The bias is a translation, not a rotation. It moves the boundary along its own normal $\vec{w}$ and cannot change which side of the plane through the origin a point sits on. Any question that requires re-orienting the boundary needs $\vec{w}$ to change, and the bias cannot help.

The tie between $P$ and $R$ is worth noting: two points at different locations can be equidistant from a boundary, because distance to a hyperplane collapses $d$ coordinates into one number.