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Linear function

If b ≠ 0, the equation

is a linear equation in the single variable y for every value of x. It has therefore a unique solution for y, which is given by

This defines a function. The graph of this function is a line with slope − a b {\displaystyle -{\frac {a}{b}}} and y -intercept − c b. {\displaystyle -{\frac {c}{b}}.} 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 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 functions, and the linear functions such that c = 0 are often called linear maps.