Cambridge International AS and A Level Mathematics Pure Mathematics 1

Finding the equation of a line

P1^

2

The line passes through (0, 6) and (8, 0).

EXERCISE 2B 1 Sketch the following lines.

(i) y = − 2 (ii) x = 5 (iii) y = 2 x

(iv) y = − 3 x (v) y = 3 x + 5 (vi) y = x − 4

(vii) y = x + 4 (viii) yx=+^122 (ix) yx=+ 2 12 

(x) y = − 4 x + 8 (xi) y = 4 x − 8 (xii) y = −x + 1

(xiii) yx=––^122  (xiv) y = 1 − 2 x (xv) 3 x − 2 y = 6

(xvi) 2 x + 5 y = 10 (xvii) 2 x +y − 3 = 0 (xviii) 2 y = 5 x − 4

(xix) x + 3 y − 6 = 0 (xx) y = 2 − x

2 By calculating the gradients of the following pairs of lines, state whether they

are parallel, perpendicular or neither.

(i) y = − 4 x = 2 (ii) y = 3 x x = 3 y

(iii) 2 x + y = 1 x − 2 y = 1 (iv) y = 2 x + 3 4 x − y + 1 = 0

(v) 3 x − y + 2 = 0 3 x + y = 0 (vi) 2 x + 3 y = 4 2 y = 3 x − 2

(vii) x + 2 y − 1 = 0 x + 2 y + 1 = 0 (viii) y = 2 x − 1 2 x − y + 3 = 0

(ix) y=x − 2 x + y = 6 (x) y = 4 − 2 x x+ 2 y= 8

(xi) x + 3 y − 2 = 0 y = 3 x + 2 (xii) y = 2 x 4 x + 2 y = 5

Finding the equation of a line

The simplest way to find the equation of a straight line depends on what

information you have been given.

y

x

(8, 0)

(0, –1)

3 x + 4y = 24

y = x – 1

(1, 0)

(0, 6)

(^0) 1 2 3 4 5 6 7 8
1
2
3
4
5
6
Figure 2.14