Everything Maths Grade 11

CHAPTER 16. GEOMETRY 16.5

y = mx + c and the equation of thesecond line is y = m 0 x + c 0 , then we know the following:

If the lines are parallel, then m = m 0 (16.12)

If the lines are perpendicular, then m× m 0 =− 1 (16.13)

Once we have determined a value for m, we can then use the given point together with:

y− y 1 = m(x− x 1 )

to determine the equation of the line.

For example, find the equation of the line that isparallel to y = 2x− 1 and that passes through (−1;1).

First we determine m, the slope of the line we are trying to find. Since the line we are looking for is
parallel to y = 2x− 1 ,
m = 2

The equation is found by substituting m and (−1;1) into:

y− y 1 = m(x− x 1 )

y− 1 = 2(x− (−1)

y− 1 = 2(x + 1)

y− 1 = 2x + 2

y = 2x + 2 + 1

y = 2x + 3

1

2

3

− 1

− 2

3 2 − − 1 − 1 2 3

(−1;1)� y = 2x− 1

y = 2x + 3

x

y

Figure 16.3: The equation of the line passing through(−1;1) and parallel to y = 2x− 1 is y = 2x+3. It
can be seen that the lines are parallel to each other. You can test this by using your ruler and measuring
the perpendicular distance between the lines atdifferent points.

Inclination of a Line EMBCN

In Figure 16.4(a), we see that the line makes anangle θ with the x-axis. This angle is known as the
inclination of the line and it is sometimes interesting to know what the value of θ is.