Cambridge International Mathematics

302 Straight lines (Chapter 14)

Example 3 Self Tutor

Find the equation of a line:

a with gradient 2 andy-intercept 5

b with gradient^23 which passes through(6,¡1).

a m=2and c=5, so the equation is y=2x+5.

b m=^23 so the equation is y=^23 x+c

But when x=6, y=¡ 1 fthe point(6,¡1)lies on the lineg

) ¡1=^23 (6) +c

) ¡1=4+c

) ¡5=c

So, the equation is y=^23 x¡ 5.

Example 4 Self Tutor

Find the equation of a line passing through(¡ 1 ,5) and (3,¡2).

The gradient of the line m=

¡ 2 ¡ 5

3 ¡¡ 1

=¡^74

) the equation is y=¡^74 x+c

But when x=¡ 1 , y=5

) 5=¡^74 (¡1) +c

) 5=^74 +c

)^204 =^74 +c

) c=^134

So, the equation is y=¡^74 x+^134.

EXERCISE 14C

1 Find the equation of a line:

a with gradient 3 andy-intercept¡ 2 b with gradient¡ 4 andy-intercept 8

c with gradient^12 andy-intercept^23 d with gradient¡^23 andy-intercept^34.

2 Find the gradient andy-intercept of a line with equation:

a y=3x+11 b y=¡ 2 x+6 c y=^12 x

d y=¡^13 x¡ 2 e y=3 f x=8

g y=3¡ 2 x h y=¡1+^12 x i y=

3 x+1

2

j y=

2 x¡ 1

3

k y=

1 ¡x

4

l y=

3 ¡ 2 x

5

O

x

y

()-1 ¡5,

()3 -2,

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Y:\HAESE\IGCSE01\IG01_14\302IGCSE01_14.CDR Friday, 26 September 2008 11:56:48 AM PETER