If a line coincides with at least two vertices on an infinite Cartesian grid, its slope is rational.
If a line coincides with only one vertex on an infinite Cartesian grid, its slope is irrational.
If a line coincides with no vertices on an infinite Cartesian grid, its slope is either irrational or rational.
If a line coincides with only one vertex on an infinite Cartesian grid, its slope is irrational.
If a line coincides with no vertices on an infinite Cartesian grid, its slope is either irrational or rational.