Question: Suppose $C$ is an affine plane curve and L is a line in $A^2(K)$, $L\not\subset C$. Suppose $C=V(F)$ and $F\in K[x,y]$ a polynomial of degree n. Show that $L\cap C$ is a finite set of no more than n points.
My attemp: Btw, I saw this question nearby similar question but I can't understand writings about the proof.
First, I don't know meaning of affine plane curve. Now, $F$ is polynomial so $V(F)$ is zero set of polynomial and $L$ is a line in $A^2$ so it is something like $y=ax+b$. If a point $(a,b)$ in $L \cap C$ then it satisfies the following $F(a,b)=0$ and we have this line $ y=ax+b$.
I am stuck with it now.
Thanks in advance