Cambridge Additional Mathematics

Straight line graphs (Chapter 7) 179

EXERCISE 7A.1

1 Find the gradient andy-intercept of the line with equation:

a y=3x+5 b y=4x¡ 2 c y=^15 x+^35

d y=¡ 7 x¡ 3 e y=x+2

6

f y=^8 ¡^5 x

3

2 Find the equation of the line with:

a gradient 1 andy-intercept¡ 2 b gradient¡ 1 andy-intercept 4

c gradient 2 andy-intercept 0 d gradient¡^12 andy-intercept 3.

3 Find, ingradient-intercept form, the equation of the line through:

a (2,¡5) with gradient 4 b (¡ 1 ,¡2) with gradient¡ 3

c (7,¡3) with gradient¡ 5 d (1,4) with gradient^12

e (¡ 1 ,3) with gradient¡^13 f (2,6) with gradient 0.

4 Find, ingeneral form, the equation of the line through:

a (2,5) having gradient^23 b (¡ 1 ,4) having gradient^35

c (5,0) having gradient¡^13 d (6,¡2) having gradient¡^27

e (¡ 3 ,¡1) having gradient 4 f (5,¡3) having gradient¡ 2

g (4,¡5) having gradient¡ 312 h (¡ 7 ,¡2) having gradient 6.

Example 3 Self Tutor

Find the equation of the line which passes through the points A(¡ 1 ,5) and B(2,3).

The gradient of the line is

3 ¡ 5

2 ¡(¡1)

=¡

2

3

.

Using point A, the equation is

y¡5=¡^23 (x¡(¡1))

) 3(y¡5) =¡2(x+1)

) 3 y¡15 =¡ 2 x¡ 2

) 2 x+3y=13

5 Find, ingradient-intercept form, the equation of the line which passes through the points:

a A(2,3) and B(4,8) b A(0,3) and B(¡ 1 ,5)

c A(¡ 1 ,¡2) and B(4,¡2) d C(¡ 3 ,1) and D(2,0)

e P(5,¡1) and Q(¡ 1 ,¡2) f R(¡ 1 ,¡3) and S(¡ 4 ,¡1).

6 Find, ingeneral form, the equation of the line which passes through:

a (0,1) and (3,2) b (1,4) and (0,¡1) c (2,¡1) and (¡ 1 ,¡4)

d (0,¡2) and (5,2) e (3,2) and (¡ 1 ,0) f (¡ 1 ,¡1) and (2,¡3).

We would get the same

equation using point B.

Try it for yourself.

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_07\175CamAdd_07.cdr Friday, 20 December 2013 1:16:17 PM BRIAN