Rational Number is Algebraic of Degree 1

Theorem
Let $r \in \Q$ be a rational number.

Then $r$ is an algebraic number of degree $1$.

Proof
Let $r$ be expressed in the form:
 * $r = \dfrac p q$

By Rational Number is Algebraic, $r$ can be expressed as the root of the linear polynomial:
 * $q x - p = 0$

A polynomial of degree zero is a constant polynomial, and has no roots.

Hence the result by definition of degree of algebraic number.