Exploring distance time graphs
Exploring distance time graphs

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Exploring distance time graphs

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, thex-axis and they-axis are often simply labelled ‘x’ and ‘y’, respectively.

Figure 19
Figure 19 The x- and y-axes of a graph

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 thex-axis, positive numbers increase to the right and negative numbers increase to the left. Similarly, on they-axis, positive numbers increase up the page, and negative numbers increase down the page.

Figure 20
Figure 20 Positive and negative axes

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, they-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 thex-axis are positive while the y-axis values are negative.

Recall that each point on a graph is represented by a pair of numbers calledcoordinates. 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.

Figure 21
Figure 21 The coordinates of a point
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