Mathematics in Cybersecurity

4Straight-Line Equations and Graphs

4.1 Introduction to Straight Lines

In mathematics, the Cartesian coordinate system provides a fundamental framework for graphing lines and visualizing relationships between two variables. Named after the mathematician René Descartes (1596–1650), this system uses two perpendicular axis lines (together referred to as axes [pronounced: ak sees]), the x-axis (horizontal) and y-axis (vertical), intersecting at a point referred to as the origin of the plane, identified as (0, 0).

The axes are number lines, with the positive values of the x-axis extending to the right, negative values to the left, and the positive values of the y-axis extending upward, negative values downward. The plane itself is a two-dimensional surface (it has no thickness whatsoever) with no boundary.

It is useful to visualize the plane as a flat surface, like a tabletop or a sheet of paper, but this serves only as a reference for us. The plane, remember, extends forever, while the tabletop or paper has only a finite surface area. Likewise, the plane has no thickness, while the tabletop and the sheet of paper do have thickness.

We present the content of this chapter with the presumption that terminology and fundamental notions of the Cartesian plane (the aforementioned x-axis, y-axis, origin, identification of the location of points using ordered pair coordinates, the quadrants, and so on) are well-understood. If you should need a review of these concepts, a text in college ...