Basic Engineering Mathematics, Fifth Edition

Straight line graphs 139

23

20

24 23 220

15

10

8

5

25

210

215

220

y

x

C

B

A

21 132 4

Figure 17.13

(b) They-axis intercept atx=0 is seen to be aty=3.

y=mx+c is a straight line graph where

m=gradient andc=y-axis intercept.

From above,m=5andc=3.

Hence, the equation of the graph isy= 5 x+ 3.

Problem 9. Determine the equation of the

straight line shown in Figure 17.14.

4

24 23 22 0

3

2

1

21

22

23

24

y

x

F E

D

21 132 4

Figure 17.14

The triangleDEFis shownconstructed in Figure17.14.

Gradient ofDE=

DF

FE

=

3 −(− 3 )

− 1 − 2

=

6

− 3

=− 2

and they-axis intercept=1.

Hence,the equation of the straight line isy=mx+c

i.e.y=− 2 x+ 1.

Problem 10. The velocity of a body was

measured at various times and the results obtained

were as follows:

Velocityv(m/s) 8 10.5 13 15.5 18 20.5 23

Timet(s) 1 2 3 4 5 6 7

Plot a graph of velocity (vertically) against time

(horizontally) and determine the equation of the

graph

Suitable scales are chosen and the co-ordinates (1, 8),

(2, 10.5), (3, 13), and so on, are plotted as shown in

Figure 17.15.

0

4

5.5

6

8 Q R

P

10

12

14

16

Velocity (

y), in metres per second

18

20

22

123

Time (t), in seconds

4567

Figure 17.15

The right-angled trianglePRQis constructed on the

graph as shown in Figure 17.15.

Gradient ofPQ=

PR

RQ

=

18 − 8

5 − 1

=

10

4

= 2. 5

Thevertical axis interceptis atv=5.5m/s.

The equation of a straight line graph isy=mx+c.In

this case,tcorresponds toxandvcorresponds toy.

Hence, the equation of the graph shown in Figure 17.15