In our section on history of analytic geometry, we have mentioned that the cartesian plane was the brainchild of mathematicians Pierre de Fermat and Rene Descartes. It was an intelligent union of algebra and geometry.

The cartesian plane is actually the graphical representation of an algebraic equation, of any form. It can show graphs of polynomials, rational functions, conic sections, hyperbolas, exponential and logarithmic functions, trigonometric functions, and even vectors. However, it cannot illustrate the complex number system.

In this section, we will introduce the idea of a cartesian plane, as well as its use to plot graphs. Also explained are the graphs of linear equations, and the solutions to simultaneous equations read from graphs.

Elements of the Cartesian Plane

• x-axis. This is the horizontal axis, where the x values are plotted along.
• y-axis. This is the vertical axis, where the y values are plotted along.
• origin. It is symbolised by 0. This marks the value of 0 of both axes, where they intersect. Hence, values to the right are positive x, to the left are negative x, upwards are positive y and downwards, negative y.
• co-ordinates. They are given in the form (x,y) and is used to represent different points on the plane.