Cambridge International Mathematics

304 Straight lines (Chapter 14)

7 Find the equation of a line:

a which has gradient^12 and cuts they-axis at 3

b which is parallel to a line with gradient 2 , and passes through the point(¡ 1 ,4)

c which cuts thex-axis at 5 and they-axis at¡ 2

d which cuts thexaxis at¡ 1 , and passes through(¡ 3 ,4)

e which is perpendicular to a line with gradient^34 , and cuts thex-axis at 5

f which is perpendicular to a line with gradient¡ 2 , and passes through(¡ 2 ,3).

8 Findagiven that:

a (3,a) lies on y=^12 x+^12 b (¡ 2 ,a) lies on y=¡ 3 x+7

c (a,4) lies on y=2x¡ 6 d (a,¡1) lies on y=¡x+3

Thegeneral formof the equation of a line is ax+by=d where a,banddare integers.

The general form allows us to write the equation of a line without the use of fractions. We can rearrange

equations given in gradient-intercept form so that they are in general form.

For example, to convert y=^23 x+4into the general form, we first multiply each term by 3 to remove the

fraction.

) 3 y=3(^23 )x+12 fmultiply by 3 g

) 3 y=2x+12

) ¡12 = 2x¡ 3 y fsubtract 12 and 3 yfrom both sidesg

) 2 x¡ 3 y=¡ 12

Likewise, an equation given in general form can be rearranged into the gradient-intercept form. This is done

by makingythe subject of the equation.

Example 5 Self Tutor

a Convert y=¡^34 x+1^12 into general form.

b Convert 3 x¡ 5 y=8 into gradient-intercept form.

a y=¡^34 x+1^12

) 4 y=4

¡

¡^34

¢

x+4

¡ 3

2

¢

) 4 y=¡ 3 x+6

) 3 x+4y=6

b 3 x¡ 5 y=8

) ¡ 5 y=¡ 3 x+8

) 5 y=3x¡ 8

) y=^35 x¡^85

D EQUATIONS OF LINES (GENERAL FORM) [7.6]

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Y:\HAESE\IGCSE01\IG01_14\304IGCSE01_14.CDR Friday, 26 September 2008 12:31:06 PM PETER