How do I convert the general form of a linear equation of two variables to slope intercept form?
More precisely, beginning with the form $ax + by + c = 0$
I have tried rearranging this for $y$, however, I am having difficulties with this. My idea is the following: use the substitution $c = -(x + y)$.
Is this correct?
We can rearrange the general form for $y$ as follows:
$$ax + by + c = 0 \space \iff \space by = -ax - c \space \iff \space y = -\frac{a}{b}x - \frac{c}b $$
Therefore the desired answer is $y = -\frac{a}{b}x - \frac{c}b$.
The interpretation of this formula is that our $y$-intercept is $-\frac{c}{b}$ and the gradient of line is $-\frac{a}{b}$. As the gradient is negative, we can conclude that this is a downward-sloping line.
Note: as we are dividing by $b$, we must assume that $b \neq 0$ for the above solution to hold. If $b = 0$, then we have $ax + c = 0$ which rearranges to $x = \frac{-c}{a}$ for $a \neq 0$.