Intuition: Mapping linear equation to axes

Question

Can someone give an intuition of how linear equations in two variable are mapped to a 2-D plots in the forms of lines ? And why are the axes perpendicular ?

I mean how come someone come with the idea of plotting the equations as line ? Axes ?

Answer 1

Descartes invented cartesian coordinates in the early 1600's. This views any point in 2D space as having 2 numerical values relative to a fixed point O (numbers on your perpendicular axes). Before Descartes there was no link between algebra and geometry (that may be an exaggeration), so that it is certainly not obvious that an equation represents a geometric object. The line 2x - 3y = 2 represents an infinite number of such points (x, y) in this Cartesian plane. For each x value there is a corresponding y value, restricted so that 2x - 3y = 2. Plot all of these points and you get the line.
Other coordinate systems without orthogonal axes are perfectly ok to describe the position of a point e.g. polar coordinates $(r, \theta)$ but are not well suited to describing straight lines.