How does $x^2+4xy-6x+4y^2-12y+9=0$ represent a straight line. I need to show $x^2+4xy-6x+4y^2-12y+9=0$ is a straight line. But I only know of a straight line in the form $y=mx+c$. Any help?

Note that
\begin{align}
0 & = x^2+4y^2+9 + 4xy-6x-12y\\
& = x^2 + (2y)^2 + (-3)^2 + 2\cdot x \cdot (2y) + 2 \cdot x \cdot (-3) + 2 \cdot (2y) \cdot (-3)\\
& = (x+2y-3)^2
\end{align}
This gives us
$$x+2y-3 = 0$$
which indeed is a straight line.
