Linear polynomial ($a_{1}x+a_0,a_1\ne 0$)

A linear polynomial in one variable over a field is $a_{1}x+a_0$ with $a_1\ne 0$, so its polynomial degree is one. It has the unique root $x=-a_0/a_1$. For example, $3x-6$ has root two.

As a function, it is affine; it is a linear map only when $a_0=0$. In several variables, an expression $a_0+{\sum }_i{a}_i{x}_i$ is a degree-one polynomial if some $a_i\ne 0$. Over a general ring, a nonzero leading coefficient need not be invertible, so the field root formula may be unavailable.