# Parallel and Perpendicular Line Calculator

## Find parallel and perpendicular lines step by step

The calculator will find the equation of the parallel/perpendicular line to the given line passing through the given point, with steps shown.

For drawing lines, use the graphing calculator.

Find the equation of the line to the line passing through the point (, )

Enter the equation of a line in any form: y=2x+5, x-3y+7=0, etc.
If you need to find a line given two points or a slope and one point, use line calculator.
To find a slope, use slope calculator.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Introducing the Parallel and Perpendicular Line Calculator, an online tool for quickly finding parallel and perpendicular lines. This calculator will help you determine their slopes and equations, as well as understand the underlying process.

## How to Use the Parallel and Perpendicular Line Calculator?

• ### Input

Begin by entering the equation of the line you have. Provide the coordinates of the specific point through which the new line (parallel or perpendicular) should pass. Select your desired line orientation: whether you want a line that's parallel or one that's perpendicular to the given line.

• ### Calculation

Once you've input all the necessary information, click the "Calculate" button.

• ### Result

The calculator will instantly display the required parallel or perpendicular line equation based on your inputs.

## What Are Perpendicular and Parallel Lines?

• Perpendicular Lines

Perpendicular lines are straight lines that form a right angle (90 degrees). In the context of the coordinate plane, if two lines with the slopes $m_1$ and $m_2$ are perpendicular, then their slopes are negative reciprocals of each other. Mathematically, it can be written as follows:

$$m_1m_2=-1$$

This means that the slope of a line perpendicular to another is the negative reciprocal of the original line's slope.

For example, suppose we have a line $\mathit{L_1}$ whose equation is $y=2x+1$. Its slope $m_1$ is $2$.