What does straight line general equation coefficients a, b, c mean This is the straight line general equation:
$\color{red}a x + \color{red}b y + \color{red}c = 0$
What does the coefficients $\color{red} a, \color{red}b, \color{red}c$ mean and what them names?
 A: Let $E$ be all the points $(x, y)$ that satisfy your equation. You expect $E$ to be a line.
However, if $a = b = 0$ then
1) if $c = 0$ any pair $(x, y)$ satisfies the equation, so $E$ is actually the whole plane.
2) if $c \neq 0$ then no pair $(x, y)$ can salvage the situation that the equation says $c = 0$, so $E$ is actually the empty set.
So let us now assume that either $a$ or $b$ is nonzero.
If $a = 0$ then you have $b y = c$, which fixes the $y$ coordinate; therefore $E$ is a line parallel to the $x$-axis and lies $c/b$ units to the north of it (to the south, if that number is negative).
A similar situation occurs if $b = 0$.
So, now assume that both, $a$ and $b$ are nonzero. Then it is more convenient to  rewrite your equation as $\frac{x}{A} + \frac{y}{B} = 1$, where $A = -c/a$ and $B = -c/b$. The new equation says: if $x = 0$ then $y = B$; if $y = 0$ then $x = A$; so the line goes through the points $(0, B)$ and $(A, 0)$.
You can see that the parameter $c$ gauges the distance of the line to the origin. 
I don't know about the names for $a$, $b$ and $c$.
But I would say $A$ is the $x$-intercept and $B$ is the $y$-intercept.
