# 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 + 3= 12.

Solution:

(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

$\begin{array}{l}\text{using gradient formula}\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ \frac{9-4}{5-\left(-1\right)}=\frac{q-\left(-5\right)}{5-\left(-7\right)}\\ \frac{5}{6}=\frac{q+5}{12}\end{array}$
60 = 6q + 30
6q = 30
q = 5