# 5.5 Parallel Lines

5.5 Parallel Lines

1. Two straight lines are
parallel if they have
If PQ // RS,
then mPQ = mRS

2. If two straight lines have
they are parallel.
If mAB = mCD
then AB // CD
Example 1:
Determine whether the two straight lines are parallel.
(a) 2y – 4x = 6
y = 2x 5
(b) 2y = 3x 4
3y = 2x + 12

Solution:
(a)
2y – 4x = 6
2y = 6 + 4x
y = 2x + 3,   m1 = 2
y = 2x 5,   m2 = 2
m1 = m2
Therefore, the two straight lines are parallel.

(b)

(B) Equation of Parallel Lines

To find the equation of the straight line which passes through a given point and parallel to another straight line, follow the steps below:

Step 1: Let the equation of the straight line take the form y = mx + c.
Step 2: Find the gradient of the straight line from the equation of the
straight line parallel to it.
Step 3: Substitute the value of gradient, m, the x-coordinate and
y-coordinate of the given point into y = mx + c to find the value
of the y-intercept, c.
Step 4: Write down the equation of the straight line in the form
y = mx + c.

Example 2:
Find the equation of the straight line that passes through the point (–8, 2) and is parallel to the straight line 4y + 3x = 12.

Solution: