The slope of a linear equation of the form $ Ax + By + C = 0 $ (general form) is given by $- \frac {A}{B} $. Could someone intuitively explain why we use this formula?
I've read that this is because the coefficient of x (coefficient of y) represent the "speed" at which x (y) increases and thus we can get the slope by dividing the "speed of x" by the "speed of y" -- but I'm afraid it's not very intuitive to me.
Why do we use this formula and how is this equivalent to the more general slope formula, $$ slope = - \frac {\text{change in y}}{\text{change in x}} $$
The general equation of an affine line is $y=mx+t$ with real values $m,t$.
Suppose you have two points on the line, say $(x_1,y_1)$ and $(x_2,y_2)$. Then when plugging in, the slope is $$m = \frac{y_2-y_1}{x_2-x_1}.$$