"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)
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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)
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and so clearing denominators to obtain
(3)
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gives the line in standard form with , , and .