Basic Engineering Mathematics, Fifth Edition

134 Basic Engineering Mathematics

20

15

10

11.8

5

 5

 3

10

 2  1 0

1.5

 31

2.2

243 x

y

Figure 17.7

straight line shown in Figure 17.7. (Note that the scales

used on thexandyaxes do not have to be the same.)

From the graph:

(a) whenx= 2 .2,y= 11. 8 ,and

(b) wheny=−3,x=− 1. 5

Now try the following Practice Exercise

PracticeExercise 67 Straight line graphs

(answers on page 347)

1. Assuming graph paper measuring 20cm by
   20cm is available, suggest suitable scales for
   the following ranges of values.
   (a) Horizontal axis: 3V to 55V; vertical
   axis: 10to 180.
   (b) Horizontal axis: 7m to 86m; vertical
   axis: 0.3V to 1.69V.
   (c) Horizontal axis: 5N to 150N; vertical
   axis: 0.6mm to 3.4mm.


2. Corresponding values obtained experimen-
   tally for two quantities are

x − 5 − 3 − 1 0 2 4

y − 13 − 9 − 5 − 3 1 5

Plot a graph ofy(vertically) againstx(hori-

zontally) to scales of 2cm=1 for the horizon-

talx-axis and 1cm=1 for the verticaly-axis.

(This graph will need the whole of the graph

paper with the origin somewhere in the centre

of the paper).

From the graph, find

(a) the value ofywhenx= 1

(b) the value ofywhenx=− 2. 5

(c) the value ofxwheny=− 6

(d) the value ofxwheny= 7

3. Corresponding values obtained experimen-
   tally for two quantities are

x −2.0 −0.5 0 1.0 2.5 3.0 5.0

y −13.0 −5.5 −3.0 2.0 9.5 12.022.0

Use a horizontal scale forxof 1cm=^12 unit

and a vertical scale foryof 1cm=2 units and

draw a graph ofxagainsty. Label the graph

and each of its axes. By interpolation, find

from the graph the value ofywhenxis 3.5.

4. Draw a graph ofy− 3 x+ 5 =0 over a range
   ofx=−3tox=4. Hence determine
   (a) the value ofywhenx= 1. 3
   (b) the value ofxwheny=− 9. 2


5. The speednrev/min of a motor changes when
   the voltageVacross the armature is varied.
   The results are shown in the following table.

n(rev/min) 560 720 900 1010 1240 1410

V(volts) 80 100 120 140 160 180

It is suspected that one of the readings taken of

the speed is inaccurate. Plot a graph of speed

(horizontally) against voltage (vertically) and

find this value. Find also

(a) the speed at a voltage of 132V.

(b) the voltage at a speed of 1300rev/min.

17.4 Gradients, intercepts and

equations of graphs

17.4.1 Gradients

Thegradient or slopeof a straight line is the ratio of

the change in the value ofyto the change in the value of

xbetween any two points on the line. If, asxincreases,

(→),yalso increases, (↑), then the gradient is positive.