Calculate the equation of a perpendicular line. Enter the equation of the original line and the point it passes through to calculate the perpendicular line equation.

## Perpendicular Line Formula

Linear lines are almost always displayed in the form of

y = mx + b

Where m is the slope and b is the y intercept. The first step in finding the equation of a line perpendicular to another is understanding the relationship of their slopes. The slope of a perpendicular line is always the inverse to the other. This means that the product of the two slopes is equal to -1.

With that in mind we can formulate the following equations.

a * m = -1

a = -1 / m

Where m is the original slope, and a is the slope of the perpendicular line. Now that we have the slope of our new line, all we need now is the y-intercept, b.

To calculate the y-intercept, we can use a similar formula to the one used to calculate the equation of a parallel line.

b = y₀ + 1 * x₀ / m

- Where b is the y intercept
- y0 is the y coordinate the line passes through
- X0 is the x coordinate the line passes through
- m is the slope of the original line.

## How to calculate a perpendicular line

Let’s look at an example of how to use these equations. First, lets assume you know the equation of the first line. It happens to be y=4x+5. Let’s also assume you know the x and y coordinates of a point that the perpendicular line passes through, say (4,5).

First, we need to calculate the slope. From the equation a = -1 / m we get a value of -1/4.

Next, we need to calculate the y intercept of the new line using the equation b = y₀ + 1 * x₀ / m . From this we get a value of 6.

Finally, we need to put this all together in the form: y=-1/4x + 6.

## Finding Parallel and Perpendicular Lines

in the 2-Dimension Cartesian Plane, all straight lines can be represented as an equation of the form y=mx+b, where m is the slope and x an y are points along the line. Since all lines can be described this way, it makes calculating parallel and perpendicular lines simple.

It’s just a matter of manipulating the equation. Let’s look at how the equation is manipulated in order to calculate the equation of a perpendicular line.

Conceptually, a perpendicular line is a line that crosses through the original line at any point an forms a 90 degree angle at intercept. Since there can be an infinite number of perpendicular lines, calculating any specific line requires a point.

The slope of a perpendicular line is the reciprocal of the slope of the original line. This simply means if the original slope is m, the reciprocal is 1/m. With this in mind, we can now manipulate the equation to determine the perpendicular line.

y=mx+b —> y2=(1/m)x2+b

The only thing left to do is solve for be using the point given along the perpendicular line.

## Steps to calculate a perpendicular line

We’ve gone over how to calculate the equation of a perpendicular line, and how manipulation of the original equation yields the results, but the following steps will outline the specific steps.

- Calculate the slope of the original line. This can be done through the use of two points along the original line. To learn more about calculating the slope of a line click here.
- Take the reciprocal of the original slope. If the slope is m, the reciprocal is 1/m.
- Calculate b, the y intercept of the new line using the new slope and the point given along that line.
- Put all of the information together in point slope form.

For more math related calculators, click here.

## Related Terms

perpendicular line calculator |

perpendicular line formula |

how to calculate perpendicular line |

how to find perpendicular bisector |

perpendicular formula |

perpendicular bisector equation |

perpendicular calculator |

perpendicular slope calculator |

perpendicular bisector calculator |

perpendicular bisector formula |

angle bisector formula |

how to find perpendicular distance |

find the equation of the perpendicular bisector |

perpendicular equation calculator |

how to find the equation of a perpendicular bisector |

perpendicular gradient formula |

perpendicular distance from a point to a line 3d formula |

equation of perpendicular bisector calculator |

how to find the perpendicular bisector of a triangle |

angle bisector calculator |

how to find the perpendicular bisector of a line |

perpendicular bisector of a line equation |

bisector formula |

find perpendicular line calculator |

find perpendicular bisector |

formula of perpendicular distance |

find the equation of the perpendicular bisector of the line segment joining the points |

perpendicular distance between a point and a line |

how to find the equation of the perpendicular bisector |

formula for perpendicular distance |

find the equation of the perpendicular bisector calculator |

bisector calculator |

how to calculate perpendicular distance |

how to calculate perpendicular bisector |

perpendicular distance calculator |

bisector equation |

perpendicular triangle formula |

perpendicular equation solver |

equation of a line perpendicular calculator |

find perpendicular distance from point to line |

find the equation of perpendicular bisector |

equation of perpendicular bisector of a line |

formula for perpendicular distance from a point to a line |

how to find the bisector of a triangle |

finding the perpendicular bisector of a line |

find the equation of a line perpendicular calculator |

perpendicular line through a point calculator |

segment bisector calculator |

perpendicular equation formula |

how to find perpendicular distance between two lines |

find the equation of the line perpendicular to the tangent line at this point |

how to find the perpendicular bisector of two points |

formula of perpendicular bisector |

perpendicular distance between two lines formula |

equation of the line perpendicular calculator |

find the equation of the line that is perpendicular to this line and passes through the point calculator |

equation of right bisector |

how to find the perpendicular distance of a point from a line |

how to write the equation of a perpendicular bisector |

equation of straight line perpendicular |

how to find the slope of a perpendicular bisector |

how to find the perpendicular |

perpendicular formula for triangle |

equation for a perpendicular bisector |

formula to find perpendicular distance |

perpendicular slope finder |

perpendicular bisector of a triangle formula |

calculate perpendicular distance from point to line |

how to find bisector of a triangle |

find the perpendicular distance of the point from the line |

line perpendicular to another line calculator |

how to calculate perpendicular |

formula for angle bisector |

how to find perpendicular distance of a triangle |

triangle perpendicular formula |

how do you find the equation of a perpendicular bisector |

finding perpendicular lines calculator |

how do you find the perpendicular bisector of a line |

how to find the bisector |

perpendicular bisector graph |

find the equation perpendicular to the line calculator |

how to find the equation of a line with one point and a perpendicular line |

equation of perpendicular line through a point calculator |

how to find the perpendicular bisector of a segment |

perpendicular line calculator with point |

equation of perpendicular bisector of two points |

how to find the slope of a line perpendicular to another line calculator |