Prove that every first degree equation in $x$ and $y$ always represents a straight line.

Question

Prove that every first degree equation in $x$ and $y$ always represents a straight line.

My Attempt: Let the first degree equation in $x$ and $y$ be $$ax+by+c=0$$. Let $A(x_1, y_1)$, $B(x_2, y_2)$ and $C(x_3,y_3)$ be any three points in the locus of the given first degree equation. Then, $$ax_1+by_1+c=0$$ $$ax_2+by_2+c=0$$ $$ax_3+by_3+c=0$$

Now, how should I complete?

Answer 1

Hint:

Show the vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are linearly dependent.