Equations of Perpendicular Lines
Key Questions

Answer:
If there is no specific point that the perpendicular line must pass through, all lines with slopes that are opposite reciprocals of the original line are perpendicular to it.
Explanation:
For example, the line
#y=3x# has a slope of 3.Any line that is perpendicular to it must be opposite (negative instead of positive or vice versa) reciprocals (multiplicative inverse, reciprocals multiply to 1, flip the numerator and denominator)
Opposite of 3: 3
Reciprocal of 3 (
#3/1# ):#1/3# Lines that are perpendicular to
#y=3x# must have a slope of#1/3# . That is the only requirement. The yintercepts can vary.Perpendicular lines to
#y=3x# :#y=1/3x+4# #y=1/3x12# #y=1/3x# The yintercepts change where the lines intersect, but all these lines are perpendicular to
#y=3x# . 
Say we have the two lines:
#"Line 1":y=m_1x+c_1#
#"Line 2":y=m_2x+c_2# If
#m_1=m_2# then the lines are parallel, since they both have the same rate of change and therefore will never cross.If
#m_1m_2=1# then they are perpendicular. 
The slopes of perpendicular lines are negative reciprocal of each other.
I hope that this was helpful.
Questions
Forms of Linear Equations

Write an Equation Given the Slope and a Point

Write an Equation Given Two Points

Write a Function in SlopeIntercept Form

Linear Equations in PointSlope Form

Forms of Linear Equations

Applications Using Linear Models

Equations of Parallel Lines

Equations of Perpendicular Lines

Families of Lines

Fitting Lines to Data

Linear Interpolation and Extrapolation

Problem Solving with Linear Models

Dimensional Analysis