Basic Engineering Mathematics, Fifth Edition

Straight line graphs 133

value outside the given data is calledextrapo-

lation.Toextrapolateweneedtohaveextended

thestraightlinedrawn.Similarly,determinethe

force applied when theload iszero. It shouldbe

close to 11N. The point where the straight line

crosses the vertical axis is called thevertical-

axis intercept.So,in this case,thevertical-axis

intercept=11N at co-ordinates (0, 11).

The graph you have drawn should look something

like Figure 17.5 shown below.

10

0 100 200 300 400 500 600 700 800

L (Newtons)

F (Newtons)

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

Graph of F against L

Figure 17.5

In another example, let the relationship between two
variablesxandybey= 3 x+2.

Whenx=0,y= 0 + 2 = 2
Whenx=1,y= 3 + 2 = 5
Whenx=2,y= 6 + 2 =8, and so on.

The co-ordinates (0, 2), (1, 5) and (2, 8) have been
produced and are plotted, with others, as shown in
Figure 17.6.
When the points are joined togethera straight line
graph results,i.e.y= 3 x+2 is a straight line graph.

17.3.1 Summary of general rules to be
applied when drawing graphs
(a) Give the graph a title clearly explaining what is
being illustrated.
(b) Choose scales such that the graph occupies as
much space as possible on the graph paper
being used.

12

y 3 x 2

y

0 x

2

4

6

8

 1

Figure 17.6Graph ofy/x

(c) Choose scales so that interpolation is made as

easy as possible. Usually scales such as 1cm=

1unit,1cm=2 units or 1cm=10 units are used.

Awkward scales such as 1cm=3unitsor1cm= 7

units should not be used.

(d) The scales need not start at zero, particularly when

starting at zero produces an accumulation of points

within a small area of the graph paper.

(e) The co-ordinates, or points, should be clearly

marked. This is achieved by a cross, or a dot and

circle, or just by a dot (see Figure 17.3).

(f) A statement should be made next toeach axis

explaining the numbers represented with their

appropriate units.

(g) Sufficient numbers should be written next toeach

axis without cramping.

Problem 1. Plot the graphy= 4 x+3inthe

rangex=−3tox=+4. From the graph, find

(a) the value ofywhenx= 2 .2 and (b) the value

ofxwheny=− 3

Whenever an equation is given and a graph is required,

a table giving corresponding values of the variable is

necessary. The table is achieved as follows:

When x=− 3 ,y= 4 x+ 3 = 4 (− 3 )+ 3

=− 12 + 3 =− 9

When x=− 2 ,y= 4 (− 2 )+ 3

=− 8 + 3 =− 5 ,and so on.

Such a table is shown below.

x − 3 − 2 − 1 0 1 2 3 4

y − 9 − 5 − 1 3 7 11 15 19

The co-ordinates(− 3 ,− 9 ),(− 2 ,− 5 ),(− 1 ,− 1 ),and

so on, are plotted and joined together to produce the