Degree of image of the canonical map

Question

Suppose $X$ is a nonhyperelliptic curve of genus $g\geq 3$. There is an embedding $X\to\mathbb{P}^{g-1}$ determined by the canonical linear system. Hartshorne states that the image of this map is a curve of degree $2g-2$. Why is this so? I know that the degree of the canonical divisor $K$ is $2g-2$, but I'm not sure why this implies that the curve has that degree as well.