Cambridge Additional Mathematics

A linear relationship between

and indicates a power

relationship between and.

lgyxlg

yx

O x

lgy

(3 2),

(15 6),

O

lgy

lgx

(3 8),

(1 2),

O

lgy

(2 1),

(6 -1),

lgx

O

lgy

lgx

(8 2),

Straight line graphs (Chapter 7) 191

6

Example 15 Self Tutor

Writeyin terms ofx, giving your answer in

the form y=a£xb, where a,b 2 Q.

The graph of lgy against lgx is linear.

The gradient is

8 ¡ 2

3 ¡ 1

=3.

) the equation is lgy¡2 = 3(lgx¡1)

) lgy¡2=3lgx¡ 3

) lgy=3lgx¡ 1

) lgy=lgx^3 ¡lg 10

) lgy=lg

μ

x^3

10

¶

) y= 101 £x^3

7 Consider the graph alongside.

a Write an equation for the line in the form lgy=mlgx+c.

b Hence writeyin terms ofx.

8 Writeyin terms ofx:

abc

a Writeyin terms ofx, giving your answer in the form

y=a£ 10 bx, where a,b 2 Q.

b Findywhen x=6.

O

lgy

lgx

(1 2),

3

O

lgy

lgx

(3 7 5),.

(7 15 5),.

4037 Cambridge

cyan magenta yellow black Additional Mathematics

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_07\191CamAdd_07.cdr Tuesday, 21 January 2014 12:11:36 PM BRIAN