5.5 Parallel Lines
(A) Gradient of parallel lines
1. Two straight lines are
parallel if they have
the same gradient.
parallel if they have
the same gradient.
If PQ // RS,
then mPQ = mRS
the same gradient, then
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:
Solution:
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: