9.2.2 Equation of Parallel Lines


(A) 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 1:
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:
4y+3x=12 4y=−3x+12 y=− 3 4 x+3 ∴m=− 3 4 At (−8,2), substitute m=− 3 4 , x=−8, y=2 into: y=mx+c 2=− 3 4 ( −8 )+c c=2−6 c=−4 ∴ The equation of the staright line is y=− 3 4 x−4.

 

(B) Equation of Parallel Lines (Sample Question)
Question 1:

















The straight lines MN and PQ in the diagram above are parallel. Find the value of q.

Solution:
If two lines are parallel, their gradients are equal.
m1 = m2
mMN = mPQ

using gradient formula y 2 − y 1 x 2 − x 1 9 − 4 5 − ( − 1 ) = q − ( − 5 ) 5 − ( − 7 ) 5 6 = q + 5 12
60 = 6q + 30
6q = 30
q = 5

 

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