The general equation or standard equation of a straight line is given by
Where and are any constants and also either or .
Convert the standard equation of line into the normal form
The procedure of converting into normal form as follows
Dividing on both sides of the equation, we have
This is equation of line in normal form, where is the length of normal form the 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 line if .
(ii) is the normal form of line if . Example: Convert the equation into normal form. We have equation of line in standard form is
Dividing by normalizing factor on both sides of the equation, we have
Compare with normal form of a line , where , and .