# Perpendicular Line Equation

How to find the linear equation that is perpendicular to the given line: definition, formula, 1 example, and its solution.

## Definition

### Definition

Perpendicular Lines are the lines that form a right angle: 90 degrees.

The red symbol is the right angle symbol.

## Formula

### Formula

m_{1}⋅m_{2} = -1

m_{1}, m_{2}: Slopes of the perpendicular lines

## Example

### Example

### Solution

It says the line is perpendicular to y = 3x + 4.

Set the slope of the line you're looking for as m.

Then, by the formula,

3⋅m = -1.

Divide both sides by 3.

Then m = -1/3.

The slope, m, is -1/3.

And the line passes through (3, 1).

So the linear equation in point-slope form is

y = (-1/3)(x - 3) + 1.

Change the linear equation to slope-intercept form.

Then y = (-1/3)x + 2.

So y = (-1/3)x + 2 is the answer.

### Graph

The purple slope line is the given line y = 3x + 4.

And the blue slope line is the answer y = (-1/3)x + 2.

y = (-1/3)x + 2 is perpendicular to y = 3x + 4.

And it passes through (3, 1).