Linearity - Linear Polynomials

Linear Polynomials

In a different usage to the above, a polynomial of degree 1 is said to be linear, because the graph of a function of that form is a line.

Over the reals, a linear equation is one of the forms:

where m is often called the slope or gradient; b the y-intercept, which gives the point of intersection between the graph of the function and the y-axis.

Note that this usage of the term linear is not the same as the above, because linear polynomials over the real numbers do not in general satisfy either additivity or homogeneity. In fact, they do so if and only if b = 0. Hence, if b ≠ 0, the function is often called an affine function (see in greater generality affine transformation).