Is the following dual transform incidence and order preserving?

I am trying to understand what it means for dual transformation to be incidence and order preserving. The开发者_如何学Python book has the following example: (a, b) => y = ax - b and = mx + b => (m, -b) which is both incidence and order preserving. If I change it a bit to the following dual transformation (a, b) => y = ax + b and the line y = mx + b => (m, b). Is this dual transform incidence and order preserving? If no why?

Just finished this for homework. Let p :=(px,py), p*:=(y=pxx+py), l: y=mx+b and l*:=(m,b). If p∈l, then py=mpx+b(1), suppose l*∈p* is true, so we have b=pxm+py(2), 1 and 2 cannot be both true unless m=0 or px=0. So this definition of duality will not follow incidence preserving. if p is above l, then py>mpx+b(3), suppose l* is above p* is true, so we have b>pxm+py(4), 3 and 4 cannot be both true at the same time. So this definition of duality will not follow order preserving.