In the general form of a straight line $Ax+By+C=0$, what does $C$ actually mean?

Question

In the general form of a straight line $Ax+By+C=0$, what does $C$ actually mean? The slope of the straight line seems to affected only by the ratio between A and B. If you take two straight line equations like $3x+6y+3=0$ and $1x+2y+3=0$. They form parallel lines but not the same line. The difference in $y$-coordinates of two points on the line at any $x$ value is not equal to $C$. So $C$ is not the $y$ intercept like we saw in $m.x+c=y$ form. Can anyone explain how the general form $Ax+By+C=0$ works. I'm a 14 year old trying to learn straight lines. Thank you. The link of the image of the graph is below. https://photos.app.goo.gl/d1uzwGqs9jSBx1DN9

Answer 1

Hint. Do some algebra to rewrite $$ Ax + By + C = 0 $$ in the form $$ y = mx + c $$ by solving it for $y$ in terms of $x$.

Then you can see how $m$ and $c$ depend on $A$, $B$ and $C$.