Prove that in PZ geometry, every PZ line has an equation of the form ax+by=c, where a, b, c are all rational numbers and a and b are not both zero.
Prove that every equation of the form ax+by=c, where a, b, and c are all rational numbers and a and b are not both zero, is in fact a PZ line.
Prove that if two distinct PZ lines m and n are not parallel in the usual Euclidean sense, then they have a PZ point in common.
In terms of the possible parallel axioms for geometry, which geometry does PZ geometry most resemble: projective, Euclidean, or hyperbolic geometry?
PZ means Pixel + Zoom geometry. The PZ points are $(x,y)$ of the coordinate plane such that $x$ and $y$ are rational numbers and the $PZ$ lines are the lines of Euclidean geometry which pass through (at least) two $PZ$ points.
I have tried using geometer's sketchpad to come up with PZ lines, but I'm not sure how to start the proof. Should I just use random variables to represent ratios for a and b? How do I show that a and b cannot be zero?