# Parallel Line Calculator

## What is a Parallel Line Calculator?

'Cuemath's Online Parallel Line Calculator' is an online tool which displays the equation of a parallel line. Cuemath's parallel line calculator helps you to find the equation of a parallel line passing through a coordinate within a few seconds.

NOTE: Enter the input values upto three digits.

## How to Use the Parallel Line Calculator?

Follow the steps given below to find the equation of a parallel line.

Step 1: Enter the inputs for the equation of the line for which the parallel line equation is to be found.
Step 2: Enter the coordinates through which the line passes.
Step 3: Click on the "Calculate" button.
Step 4: Click on "Reset" button to find the equation of a parallel with a different line equation and coordinates.

## What is Meant by Parallel Line?

Two or more lines which lie on the same plane and never intersect or meet each other are known as parallel lines. To find the equation of a line which is parallel to another line, we write the given equation of the line in terms of  ' y = mx + b '

Here 'y' is the line, 'x' is the slope of the line and 'b' is the point where the line intercepts the y-axis.

Now, find the slope of the line which is parallel to the given line by taking the same value of the slope of the given line 'y=mx +b', which will be 'm1=m'. Then find the value of 'b' by substituting the coordinate points (x,y) through which the parallel line passes through. Make the equation of the parallel line with values of m1 and b values in the form of 'y = m1x + b'.

Let us understand this with an example given below.

### Solved Example:

Find the equation of the line that is parallel to the line y -2 x = 6, passing through the points (-3,5).

### Solution:

Step 1:

Rewrite the given equation in the form of 'y = mx + b'.

y - 2 x = 6
y = 6 + 2 x
or
y = (2 × x) + 6

Therefore slope (m) = 2

Step 2 :

The slope for the parallel line is same as the given line.

Slope m = 2
Parallel line's  slope (m1) = 2

Step 3:

The parallel line passes through the coordinates (-3,5) with slope value equal to 2.

Therefore the equation becomes,

5 = (2 × -3) + b
b = 11

Step 4 :

The equation of the parallel line is

y = (2 × x) + 11
y = 2 x +11

Find the parallel line equation of the following lines.

1) 2x -y = 10, passing through the coordinates (3,4).

2) -3x + y = 4, passing through the coordinates (-1,3).