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

m1⋅m2 = -1

m1, m2: 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).