# Perpendicular Line Calculator

**Perpendicular Line Calculator** is an online tool that calculates and displays the equation of a perpendicular line.

## What is a Perpendicular Line Calculator?

Perpendicular Line Calculator helps you to easily find the equation of a perpendicular line within a few seconds.

### Perpendicular Line Calculator

**NOTE:** Enter numbers up to 2 digits only.

## How to Use the Perpendicular Line Calculator?

Follow the steps given below to use the calculator:

**Step 1 :**Enter the values for the equation of the line and the coordinates in the respective input boxes.**Step 2 :**Click on**"Calculate"**to get the equation of the perpendicular line.**Step 3 :**Click on**"Reset"**to clear the fields and enter the new values.

## What is Meant by Equation of a Perpendicular Line?

When two lines intersect at right angles (90°), we call them perpendicular lines. To find the equation of a line which is perpendicular to another line:

- 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.
- In order to find the slope of the line which is perpendicular to the given line, first, take the negative reciprocal of the given line 'y = mx + b',
- Then, find the value of 'b' by substituting the coordinate points (x,y) through which the perpendicular line passes.
- Finally, form the equation of the perpendicular line by substituting the values of
**'**(-1/m) and 'b'**.**

Let us understand this with the following example.

**Solved Examples on Perpendicular Line Calculator**

**Example 1:**

Find the equation of the line that is perpendicular to the line 3y - x = 6, passing through the points (4,2).

**Solution:**

**Step 1:**

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

3y - x = 6

3y = 6 + x

y = (6/3) + (x/3)

y = 2 + (x/3) or y = ((1/3) × x) + 2

Therefore, slope (m) = 1/3

**Step 2 :**

Find the negative reciprocal of the slope.

Slope = 1/3; Negative reciprocal of slope (m) = -3

**Step 3:**

The perpendicular line passes through the coordinates (4,2) with slope value equal to -3.

Therefore, the equation becomes: 2 = ((-3) × 4) + b

After solving the equation, we get b = 14

**Step 4 :**

The equation of the perpendicular line is: y = ((-3) × x) + 14

y = -3x + 14

Now, try the perpendicular line calculator to find the perpendicular line equation of the following lines.

**Example 2:**

Find the equation of the line that is perpendicular to the line 5x - y = -12, passing through the points (3, 7).

**Solution:**

**Step 1:**

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

5x - y = -12

y - 5x = 12

y = 5x + 12

Therefore, slope (m) = 5

**Step 2 :**

Find the negative reciprocal of the slope.

Slope = 5; Negative reciprocal of slope (m) = -1/5

**Step 3:**

The perpendicular line passes through the coordinates (3, 7) with slope value equal to -1/5.

Therefore, the equation becomes: 7 = ((-1/5) × 3) + b

After solving the equation, we get b = 38/5

**Step 4 :**

The equation of the perpendicular line is: y = ((-1/5) × x) + 38/5

y = (-1/5)x + 38/5

Now, try the perpendicular line calculator to find the perpendicular line equation of the following lines.

- 5x + 6y = 10, passing through the coordinates (2,3).
- 2x + y = 4, passing through the coordinates (1,2).

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