# Perpendicular Lines

How to solve perpendicular lines problems (linear equations): definition, formula, examples, and their solutions.

## Definition, Formula

Perpendicular lines are lines

that form a right angle (= 90º).

The red symbol is the right angle symbol.

It shows that

the intercepted lines are perpendicular.

If two perpendicular lines' slopes are *m*_{1} and *m*_{2},

then *m*_{1}⋅*m*_{2} = -1.

## Example 1

See the given line.

The change of *x* is 2.

And the change of *y* is 1.

So the slope of the line is*m* = 1/2.

Slope of a line

And it says

the given line [slope: 1/2]

and *y* = *qx* - 2 [slope: *q*]

are perpendicular lines.

So (1/2)⋅*q*= -1.

Multiply 2 on both sides.

Then *q* = -2.

Let's see the graph of the parallel lines.

The increasing line is the given line.

And the decreasing line is *y* = *qx* - 2,

which is *y* = -2*x* - 2.

Its slope is -2.

And its *y*-intercept is -2.

So you can easily draw *y* = -2*x* - 2.

Slope-intercept form - Example 2.

These two lines are perpendicular.

So you can use the right angle symbol (red).

## Example 2

The slope of *y* = 3*x* + 4 is 3.

So set *m*_{1} = 3.

It says

the linear equation is perpendicular to *y* = 3*x* + 4.

[slope: 3]

Set *m*_{2} as the slope of the linear equation.

[slope: *m*_{2}]

Then 3⋅*m*_{2} = -1.

Multiply 3 on both sides.

Then *m*_{2} = -1/3.

The slope of the line is -1/3.

And it says

the line passes through (3, 1).

Then the linear equation in point-slope form

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

Change the linear equation

in slope-intercept form.

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

Let's see the graph of the perpendicular lines.

The increasing line is the given line:*y* = 3*x* + 4.

And the decreasing line is the answer:*y* = (-1/3)*x* + 2.

It is perpendicular to the given line.

And it passes through (3, 1).

These two lines are perpendicular.

So you can use the right angle symbol (red).