Cambridge Additional Mathematics

196 Straight line graphs (Chapter 7)

Example 17 Self Tutor

x 1 2 3 4

y 14 10 10 11

This table shows experimental data values forxandy:

By plotting a suitable straight line graph, show thatyandxare related

by the equation y=ax+

b

x

.

If y=ax+b

x

, then

xy=ax^2 +b

) ifyandxare related in this way, then we should observe

a linear relationship betweenxyandx^2.

x^214916

xy 14 20 30 44

The graph ofxyagainstx^2 is linear.

Using points (1,14) and (4,20),

the gradient is

20 ¡ 14

4 ¡ 1

=2.

) the equation is xy¡14 = 2(x^2 ¡1)

) xy¡14 = 2x^2 ¡ 2

) xy=2x^2 +12

) y=2x+

12

x

fa=2, b=12g

6 This table shows experimental values ofxandy: x^1234

y 1 26 99 244

It is known thatxandyare related by the equation y=ax^3 +bx, whereaandbare constants.

a A straight line graph is to be drawn to represent this information. If

y

x

is plotted on the vertical

axis, which variable should be plotted on the horizontal axis?

b Draw the straight line graph.

c Find the values ofaandb.

d Findywhen x=5.

7 This table shows experimental values ofxandy: x^1234

y 4 1 : 17 0 : 36 0

By plotting a suitable straight line graph, show thatxandyare related by the equation y=

a

x

+

b

p

x

.

xy

x 2

O 24681012 14

10

20

30

40

50

16 18

(16 44),

(9 30),

(4 20),

(1 14),

There may be more than one

way to transform the variables.

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_07\196CamAdd_07.cdr Friday, 4 April 2014 11:54:12 AM BRIAN