Cambridge International AS and A Level Mathematics Pure Mathematics 1

Finding the equation of a line

P1^

2

SOLUTION

The line 2y = x + 12 has gradient^12 and passes through the point (0, 6)

(since dividing by 2 gives y = 12 x + 6).

The line y = 4 x − 10 has gradient 4 and passes through the point (0, −10).

The other two sides are lines with gradients^12 and 4 which pass through (0, 0),

i.e. y = 12 x and y = 4 x.

EXAMPLE 2.10 Find the equation of the perpendicular bisector of the line joining P(−4, 5) to
Q(2, 3).

SOLUTION

y = 4x – 10

2 y = x + 12

(0, –10)

x

y

O

(0, 6)

The dashed lines

are the other

two sides.

Figure 2.21

y

x

P(–4, 5)

Q(2, 3)

R

O

Figure 2.22