# 1.5 Mathematical graphs

## 1.5.1 Mathematical graphs: special terms

Mathematicians use some special terms to talk about graphs. Understanding and feeling confident with this graphical language is as much a part of mathematics as doing calculations, or working with formulas. By convention, the horizontal axis of a graph – the one running across the page from left to right – is often called the ‘*x*-axis’, and the vertical axis – the one running up the page – is called the ‘*y*-axis’, as in Figure 19. As a reminder, the*x*-axis and the*y*-axis are often simply labelled ‘*x*’ and ‘*y*’, respectively.

When only positive quantities are plotted, the two axes are conventionally drawn on the left-hand and bottom edge of the graph. However, you might want to plot negative values as well. As Figure 20 shows, both axes can be extended in a negative as well as a positive direction. This follows a mathematical convention about representing numbers as points on a line; on the*x*-axis, positive numbers increase to the right and negative numbers increase to the left. Similarly, on the*y*-axis, positive numbers increase up the page, and negative numbers increase down the page.

Using negative as well as positive axes divides a graph up into four regions, called ‘quadrants’. The prefix ‘quadr-‘ as in *quadrilateral, quadrangle* and *quadrant* indicates four-ness. In Figure 20, the quadrants are numbered from 1 to 4. The convention is that the numbering goes in an anticlockwise direction. In the first quadrant, the *x*-axis and *y*-axis both represent positive values. In the second quadrant, the*y*-axis values remain positive but values along the *x*-axis are negative. In the third quadrant, both the *x*- and *y*-axes mark negative values. In the fourth quadrant, values along the*x*-axis are positive while the *y*-axis values are negative.

Recall that each point on a graph is represented by a pair of numbers called*coordinates*. Look at Figure 21. The position of the point measured along the *x*-axis is called, not surprisingly perhaps, the *x-coordinate*, and the position measured along the *y*-axis is called the *y-coordinate*. In some mathematics books you may come across the terms ‘abscissa’ for the *x*-coordinate and ‘ordinate’ for the *y*-coordinate. Coordinates which locate a point by referring to its position relative to two (or three) axes intersecting at right angles are called Cartesian coordinates.