Cambridge Additional Mathematics

Straight line graphs (Chapter 7) 181

Example 5 Self Tutor

Find the equation connecting

the variables.

(0,2) and (4,8) lie on the straight line.

) the gradient m=

8 ¡ 2

4 ¡ 0

=^64 =^32 , and the

y-intercept c=2.

In this caseKis on the vertical axis andtis on the

horizontal axis.

) the equation is K=^32 t+2.

9 Find the equation connecting the variables:

abc

de f

Example 6 Self Tutor

Consider the points A(¡ 2 ,5) and B(1,3). A line perpendicular to AB, passes through B.

a Find the equation of the line.

b Find the coordinates of the point where the line cuts thex-axis.

a The gradient of AB=

3 ¡ 5

1 ¡(¡2)

=¡^23

) the perpendicular line has gradient^32 ,

and passes through B(1,3).

) its equation is y¡3=^32 (x¡1)

) 2(y¡3) = 3(x¡1)

) 2 y¡6=3x¡ 3

) 3 x¡ 2 y=¡ 3

K

t

(4 8),

2

O

p

M

2

gradientQe

O

z

H

4

2

O

x

T

2

-1

O

x

F

(10 2),

1

O

n

R

(4, -3)

2

O

t

W

(6 -3),

-2

O

y

O x

A,(-2 5)

B,(1 3)

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_07\181CamAdd_07.cdr Monday, 6 January 2014 11:52:31 AM BRIAN