(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.
Find the equation of the straight line that passes through the point (–8, 2) and is parallel to the straight line 4y + 3x = 12.
(B) Equation of Parallel Lines (Sample Question)
The straight lines MN and PQ in the diagram above are parallel. Find the value of q.
If two lines are parallel, their gradients are equal.
m1 = m2
mMN = mPQ
60 = 6q + 30
6q = 30
q = 5