Editing Linear equation (section)

===Linear function===
{{main|Linear function (calculus)}}
If {{math|''b'' ≠ 0}}, the equation 
:<math>ax+by+c=0 </math>
is a linear equation in the single variable {{mvar|y}} for every value of {{mvar|x}}. It therefore has a unique solution for {{mvar|y}}, which is given by 
:<math>y=-\frac ab x-\frac cb. </math>

This defines a [[function (mathematics)|function]]. The [[graph of a function|graph]] of this function is a [[line (geometry)|line]] with [[slope (mathematics)|slope]] <math>-\frac ab </math> and [[y-intercept|{{mvar|y}}-intercept]] <math>-\frac cb. </math> The functions whose graph is a line are generally called ''linear functions'' in the context of [[calculus]]. However, in [[linear algebra]], a [[linear function]] is a function that maps a sum to the sum of the images of the summands. So, for this definition, the above function is linear only when {{math|1=''c'' = 0}}, that is when the line passes through the origin. To avoid confusion, the functions whose graph is an arbitrary line are often called ''[[affine function]]s'', and the linear functions such that {{math|1=''c'' = 0}} are often called ''[[linear map]]s''.