Parallel Lines Formula
The parallel lines formula is used to find whether two lines are parallel or not. The parallel line formula is applicable when we have the slope of two lines that we want to compare. Distance between the parallel lines never changes.
Let us learn more about the parallel lines formula along with solved examples.
What Is Parallel Lines Formula?
For any two lines with equations \(y = m_1x+ c_1\) and \(y = m_2x + c_2\), the formula to know that the lines are parallel is:
\(m_1 = m_2\)
where,
m_{1} and m_{2} are the slopes of the two lines.
Solved Examples Using Parallel Lines Formula

Example 1:
Find out whether the lines 2y  4x 10 = 0, and y = 2x + 27 are parallel or not.
Solution:
To Find: Parallel lines
Given:
Equation of line 1: 2y  4x 10 = 0
On rearranging and dividing by 2, we get
y = 2x + 5
On comparing with \(y = m_1x+ c_1\)
\(\implies m_1 = 2\)
Now, equation of line 2: y = 2x + 27
On comparing with \(y = m_2x+ c_2\)
\(\implies m_2 = 2\)
Using the parallel line formula, for lines to be parallel,
\(m_1 = m_2 = 2\)
Answer: Hence, the given lines are parallel. 
Example 2:
Find the slope of the second line which is parallel to the line is 12x + y + 90 = 0.
Solution:
To Find: Slope(m_{2})
Given:
Equation of line 1: 12x + y + 90 = 0
On rearranging, we get
y = 12x  90
On comparing with \(y = m_1x+ c_1\)
\(\implies m_1 = 12\)
Using the parallel line formula, for lines to be parallel,
\(m_1 = m_2 = 12\)
Answer: Hence, the slope of the given line is 12.