Cambridge International Mathematics

Straight lines (Chapter 14) 305

EXERCISE 14D.1

1 Convert the following straight line equations into general form:

a y=^12 x+3 b y=¡ 2 x+7 c y=¡^13 x¡ 2 d y=

2 x+1

3

2 Convert the following into gradient-intercept form:

a x+2y=8 b 2 x+5y=10 c 3 x¡y=11 d x+4y=6

e 6 x¡ 5 y=15 f 4 x+3y=12 g 9 x¡ 2 y=18 h 5 x+6y=30

3 Find the gradient andy-intercept of the lines with equations:

a x+3y=6 b x¡ 4 y=¡ 8 c 3 x+5y=5 d 4 x¡y=8

e x+5y=4 f 7 x¡ 5 y=¡ 15 g 4 x+3y=24 h ax¡by=d

4 Find, in general form, the equation of a line with:

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

c gradient^12 andy-intercept^14 d gradient¡^13 andy-intercept 0

e gradient¡^34 andy-intercept 2 f gradient^25 andy-intercept¡ 1.

5 Find, in general form, the equations of the illustrated lines:

abc

de f

6 Findkif:

a (2,k) lies on 2 x+y=7 b (3,k) lies on x+2y=¡ 1

c (k,1) lies on 3 x+2y=8 d (k,¡3) lies on 2 x¡ 3 y=5.

FINDING THE GENERAL FORM EQUATION OF A LINE QUICKLY

Suppose we are given the gradient of a line and a point which lies on it. Rather than finding the equation

in gradient-intercept form and then converting it to general form, there is a faster method.

If a line has gradient^34 , it must have form y=^34 x+c:

) 4 y=3x+4c

) 3 x¡ 4 y=d wheredis a constant.

If a line has gradient¡^34 , using the same working we would obtain 3 x+4y=d:

x

y

3

5

O

x

y

2 ()3 ¡4,

O

x

y

()-2 ¡3,

()1 ¡6,

O

x

y

()4 ¡3,

-2

O

x

y

-3

()4 -5,

O

x

y

-2

()-5 ¡5,

O

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Y:\HAESE\IGCSE01\IG01_14\305IGCSE01_14.CDR Friday, 26 September 2008 12:36:18 PM PETER