# Converting Linear Equations in Standard Form to Normal Form

The general equation or standard equation of a straight line is:

Where and are constants and either or .

Convert the standard equation of line into the normal form

The procedure of converting the equation into the normal form is as follows:

Dividing both sides of the equation by we have

This is the equation of the line in normal form, where is the length of the normal form origin of the line. Since the length of the normal form origin to the line must be positive, so:

(i) is the normal form of the line if .

(ii) is the normal form of line if .

Example: Convert the equation into normal form.

The equation of a line in standard form is

Dividing both sides of the equation by the normalizing factor , we have

Compare with the normal form of a line , where , and .