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Parallel and Perpendicular line calculator

Ax + By + C = 0

Input Point


Table of Content


The parallel and perpendicular line calculator finds equations for a parallel and perpendicular line that passes from a specific point and also shows their graphic representation. Explore more by reading on!

What are Parallel and Perpendicular Lines?

“Parallel lines are lines that do not intersect each other and on the other hand, perpendicular lines are two lines that intersect each other at 90 angle”.

By using a parallel line calculator you can find the equation of a line that passes through a point. Hence, here take a quick look at their attributes. 

Properties of Perpendicular and Parallel Lines:

  • Perpendicular lines have no equal corresponding angles while parallel has.
  • Perpendicular lines intersect each other while parallel lines have no intersection at any point 
  • Perpendicular lines make a right angle on the other hand parallel lines have no angle 
  • Perpendicular lines have no alternate interior angle while parallel lines have 


To find the parallel and perpendicular lines first keep in view the following formula: 

Y = ax + b


  • x and y are the coordinates
  • a and b are the coefficients 

How to Calculate the Slope of Lines? 

An online perpendicular slope calculator plots an equation that passes from a certain point or gradient between two points in the Cartesian coordinate plane. 

Find the Slope of Perpendicular Lines: 

If there are two lines “a” and “m” that are perpendicular to each other then the product of slopes is -1. As we already know the line of the equation proves the slope of perpendicular lines.

a * m = -1
a = -1 / m

Insert this in the line equation y = ax + b

y = -1/m . x + b

b = y + 1 / m . x

This is the coefficient b which is also known as the y-intercept  

Find the Slope of Parallel Lines: 

By using the parallel and perpendicular line calculator find the slope If there are two lines that are parallel to each other. As we know the equation:

Y = ax + b

When you plug in the coordinates (xj,yj) and a = m then the equation line will be:

Yj = m . xj + b

Example # 1:

Suppose a line is passing through a point (-13, 3) and parallel to y = 2x - 6. Find out the parallel and perpendicular lines equations by perpendicular line equation calculator.


Given Data:

Slope-intercept of the equation of a line is: y = 2x - 6y 

The parallel line of the slope is the same: m = 2

So, the parallel line equation is y = 2x + a 

To find a, the line should pass through a given point:

3 = (2) * (-13) + a 

a = 3 + 26

a = 29

Consequently, the equation of the line is y = 2x +29         

parallel perpendicular calculator      

Example # 2:

Suppose that the same line passes from points (-10, 3) but is perpendicular at y = 4x + 3. Find their slope-intercept form.


The slope-intercept of the equation of a line is y = 4x + 3

The slope of the perpendicular line is referred to as a negative inverse m = -1 / 4

So, the perpendicular line equation is y = -1 / 4x + a

To find a, the line should pass through a given point: 

3 = -1 / 4 * (-10) + a

a = 1 / 2 

Consequently, the equation of the line is y = 1 / 2 - x / 4

parallel perpendicular calculator

Working of Parallel and Perpendicular Line Calculator:

The perpendicular calculator allows you to find the equation for parallel and perpendicular lines fast and accurately! Providing the following values is required to make it work:


  • Choose the form of a line 
  • Select what to compute parallel either perpendicular 
  • Insert the values according to the selection
  • Tap on “Calculate”


Our slopes of parallel and perpendicular lines calculator gives you the following results:

  • Parallel line equation
  • Line interception points 
  • Equation of a line
  • Graphically representation
  • Step-by-step calculations  


Do Perpendicular Lines Have the Same Slopes?

Perpendicular lines do not have the same slope. Their slopes are different from one another. 

Why Slope of the Perpendicular Line is Negative Reciprocal?

Perpendicular lines have negative reciprocal slopes because when there are two lines that are perpendicular to each other it is almost as the rise as run switched places therefore one line has an opposite reciprocal slope to the other perpendicular line.

Which Type of Shape has four Pairs of Parallel Lines?

A “parallelogram” is a shape that has four pairs of parallel lines.

What is Zero (0) Slope Mean?

A line with a zero slope is flat in the horizontal direction and it means there is no change in the x and y coordinates 


From the source Wikipedia: Foot of a perpendicular, Construction of the perpendicular, In relationship to parallel lines, Euclidean parallelism.


Sarah Taylor

I am a professional Chemist/Blogger & Content Writer. I love to research chemistry topics and help everyone learning Organic & Inorganic Chemistry and Biochemistry. I would do anything to spend vacations on a Hill Station.

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