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The general form for
: <math> Ax+By=C. </math>
When <math> B \ne 0 </math> this equation may be solved for the variable {{mvar|y}} and thus used to define a linear function (namely, <math> y = - \tfrac{A}{B} x + \tfrac{C}{B} = f(x)</math>). While all lines have equations in the general form, only the non-vertical lines have equations which can give rise to linear functions.
The general form has 2 variables {{mvar|x}} and {{mvar|y}} and 3 coefficients {{mvar|A}}, {{mvar|B}}, and {{mvar|C}}.
This form is not unique. If one multiplies {{mvar|A}}, {{mvar|B}} and {{mvar|C}} by a constant factor {{mvar|k}}, the coefficients change, but the line remains the same. The linear function obtained from this form is unique since it depends only on the coordinates of the points on the line. For example, {{math|1=3''x'' − 2''y'' = 1}} and {{math|1=9''x'' − 6''y'' = 3}} are general forms of the equation of the same line which is associated with the linear function <math> f(x) = \tfrac{3}{2} x - \tfrac{1}{2} </math>.
This general form is used mainly in geometry and in systems of two linear equations in two unknowns.
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