Basic Engineering Mathematics, Fifth Edition

Straight line graphs 131

1

2

3

4

5

A B C D E F

Figure 17.2Reprinted with permission from AA Media Ltd.

a point on a map. If you are familiar with using a
map in this way then you should have no difficulties
with graphs, because similar co-ordinates are used with
graphs.
As stated earlier, agraphis a visual representation
of information, showing how one quantity varies with
another related quantity. The most common method of
showing a relationship between two sets of data is to
use a pair of reference axes – these are two lines drawn
at right angles to each other (often calledCartesianor
rectangular axes), as shown in Figure 17.3.
The horizontal axis is labelled thex-axis and the ver-
tical axis is labelled they-axis. The point wherexis 0
andyis 0 is called theorigin.
xvalues havescalesthat are positive to the right of
the origin and negative to the left.yvalues have scales
that are positive up from the origin and negative down
from the origin.
Co-ordinatesare written with brackets and a comma
in between twonumbers. For example, pointAis shown
with co-ordinates (3, 2) and is located by starting at the

A(3, 2)

4

242322210

3

2

1

21

22

23

24

Origin

C( 2 3, 2 2)

B ( 2 4, 3)

y

(^1342) x
Figure 17.3
origin and moving 3 units in the positivex direction
(i.e. to the right) and then 2 units in the positivey
direction (i.e. up).
When co-ordinates are stated the first number is
always thex value and the second number is always