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,

m₁ and m₂ 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 a line that is parallel to the line is 12x + y + 90 = 0.

Solution:

To Find: Slope of a line parallel to 12x + y + 90 = 0.

Given: 

Equation of the given line: 12x + y + 90 = 0

On rearranging, we get y = -12x - 90

On comparing with \(y = m_1x+ c_1\), we get the slope = -12

By the parallel line formula, for lines to be parallel, their slopes are equal.

 Therefore, the slope of every line parallel to this line would have to be m = -12

Answer: Hence, the slope of the line parallel to the given line is -12.