What is the effect of the bias parameter in the hyperplane function

Question

When we are dealing with Hyperplanes in Support Vector Machines,what is the effect of b, the bias.

wTx+b=0

Lets say I have a 1D Hyperplane on a 2D plane of (X,Y) that runs through y=5. So a straight line orthogonal to the X. what is the effect of b. If I go b=b+1 does it move vertically to y=6 or does it rotate around? I'm trying to understand visually what its doing to the line.

Answer 1

Changing bias will result in parallel shift of your hyperplane. Namely the hyperplanes $w^Tx+b_1 = 0$ and $w^Tx+b_2 = 0$ are parallel. To exploit some visual intuition, one can consider $2d$-plane. See the picture, where shaded lines are created by changing bias of the solid line.