Someone please explain, what is the purpose of the normal form of a linear equation. Supposedly the linear form is supposed to be perpendicular to the standard form, but when we take this equation:

2x+y-5=0

The normal form is:

(2√5)/5x+√5/5y-√5=0

How is that perpendicular? None of the signs have changed. I'm beyond confused.

I know how to do these equations, I just don't understand this aspect.

Question

Someone please explain, what is the purpose of the normal form of a linear equation. Supposedly the linear form is supposed to be perpendicular to the standard form, but when we take this equation:

2x+y-5=0

The normal form is:

(2√5)/5x+√5/5y-√5=0

How is that perpendicular? None of the signs have changed. I'm beyond confused. 

I know how to do these equations, I just don't understand this aspect.

agent0smith · Answer

I don't think it's meant to be a perpendicular line - it's about finding the distance from the origin to the line. This may help: http://doubleroot.in/straight-line-normal-form/