Cambridge Additional Mathematics

180 Straight line graphs (Chapter 7)

7 Consider the points A(2,5) and B(¡ 4 ,2). Find:

a the distance between A and B

b the midpoint of AB

c the gradient of the line which passes through A and B

d the equation of the line which passes through A and B.

Example 4 Self Tutor

Find the equation of the line with graph:

ab

a Two points on the line are (0,1)

and (5,4).

) the gradient m=

4 ¡ 1

5 ¡ 0

=^35

and they-intercept c=1.

The equation is y=^35 x+1

fgradient-intercept formg

b Two points on the line are (2,4)

and (6,¡1).

) the gradient m=

¡ 1 ¡ 4

6 ¡ 2

=¡^54

Since we do not know they-intercept

we use the general form.

The equation is y¡4=¡^54 (x¡2)

) 4(y¡4) =¡5(x¡2)

) 4 y¡16 =¡ 5 x+10

) 5 x+4y=26

8 Find the equations of the illustrated lines:

abc

de f

y

x

1

(5 4),

O

y

x

(2 4),

(6 -1),

O

(3 3),

-1

O

y

x

(2 3),

1

O

y

x

-3

(4 -3),

O

y

x

(-2 3),

(1 5),

O

y

x

2

O^3

y

-1 x

(-3 4),

O

y

x

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_07\180CamAdd_07.cdr Monday, 6 January 2014 11:52:08 AM BRIAN