9.2 Gradient of Parallel Lines

9.2.1 Parallel Lines
 
(A) Gradient of parallel lines

1. Two straight lines are 
parallel if they have
the same gradient.
If PQ // RS,
then mPQ = mRS
   
2. If two straight lines have 
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
= 2x + 3,   m1= 2
= 2x 5,   m2 = 2
m1= m2
Therefore, the two straight lines are parallel.
 
(b)
2y=3x4 y= 3 2 x2,    m 1 = 3 2 3y=2x+12 y= 2 3 x+4,    m 2 = 2 3 m 1 m 2  The two straight lines are not parallel.

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