For two lines, where m₁ is the slope of one line and m₂ is the slope of the second line, the two lines are

• parallel if m₁ = m₂.
   
• perpendicular if m₁ × m₂ = -1.
  In this case, m₁ and m₂ are called negative reciprocals.

Example 1: Perpendicular slope

What slope is perpendicular to slope 5/2?

To find the perpendicular slope, find the negative reciprocal of 5/2.

1.	Flip the slope to get the reciprocal
	5 2   →   2 5
2.	Reverse the sign to get the negative reciprocal
	2 5   →   - 2 5
The negative reciprocal of 5/2 is -2/5.

The answer is

Example 2: Find the equation of a line

In slope-intercept form, write the equation of the line that intersects (2, -4) and is perpendicular to x + 3y = 0
Equation:

1. Find the slope perpendicular to x + 3y = 0

A line equation with the form ax + by = c, the slope m =	- a b
The line x + 3y = 0 has a slope m =	- 1 3
Therefore, the line perpendicular to x + 3y = 0 has a slope m1 =	3

2. Knowing the slope and intersection point, find the equation of the perpendicular line

The slope m₁ = 3 and a point on the line (x, y) = (2, -4)

y	=	mx + b
-4	=	3(2) + b
-4	=	6 + b
-10	=	b

Plugging the values for m and b into the slope-intercept formula, we get the answer