"Standard form" is a general term used in mathematics to refer to a normalized form of an expression. The term "canonical form" is also used in certain contexts (for example, graphs).
The standard form of a line in the Cartesian plane is given by
 |
(1)
|
for real numbers 
.
This form can be derived from any of the other forms (point-slope form, slope-intercept form, etc.), but
can be seen most intuitively when starting from intercept
form. Indeed, the intercept form of a line with x-intercept 
and y-intercept 
is given by
 |
(2)
|
and so clearing denominators to obtain
 |
(3)
|
gives the line in standard form with 
, 
,
and 
.
