# Parallel Line Formula

Two lines are said to be parallel if they always maintain 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 as Equidistant.

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 *(x**1, y1**),* slope should *be **−ab**−ab*. 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.

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

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

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

### Solved Examples

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

**Solution:**

The given equation is,

6x – 3y = 2 and the coordinates are (1, 2)

$Slope=\frac{-a}{b}$

$m =\frac{-a}{b}$ = $\frac{-6}{-3}= 2$

Parallel line equation is,

y – y_{1} = m (x – x_{1})

y – 2 = 2 (x – 1)

y – 2 = 2x – 2

y = 2x – 2 + 2 = 2x