Parallel Line Formula

Parallel Line Formula

Two lines are said to be parallel if they always maintain the same distance apart. If two lines are drawn so that they could extend into infinity without ever meeting each other, these lines are called parallel. Parallel lines are also called Equidistant lines.

Lines which will never intersect each other are parallel. If angles are considered then it is 180 degrees, here the two lines are equal so they will never meet.

We need to find out the slope first from the given equation. Then, substitute the straight-line equation and find out the value of y. If the equation of the line is ax + by + c = 0 and coordinates are (x1, y1), the slope should be -a/b. If two lines are parallel to each other, the slopes of both line are equal. Consider m1 and m2 be the slopes of the two lines. 

\[\large Parallel\;Lines=m_{1}=m_{2}\]

To find out the parallel line of a given line with slope m and which is passing through a point (x1, y1), the given formula is used.

\[\large Slope=\frac{-a}{b}\]

\[\large Parallel\;Lines\;Equation: y-y_{1}=m(x-x_{1})\]

Solved Example

Question: Find out the parallel line of the given straight line 6x – 3y = 2 passing through a point (1, 2).


The given equation is,
6x – 3y = 2 and the coordinates are (1, 2)

\(\begin{array}{l}Slope=\frac{-a}{b}\end{array} \)

\(\begin{array}{l}m =\frac{-a}{b}\end{array} \)
\(\begin{array}{l}\frac{-6}{-3}= 2\end{array} \)

(x1, y1) = (1, 2)

Parallel line equation is:

y – y1 = m (x – x1)
y – 2 = 2 (x – 1)
y – 2 = 2x – 2
y = 2x – 2 + 2

y = 2x


2x – y = 0


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