Q:

How does $x - 4y = 12$ result in $y = \frac{1}{4}x - 3$ instead of $y = -\frac{1}{4}x - 3$?

I'm learning math. That's why I'm asking a simple explanation from a math expert.
When I solve this equation it results in $y = -\frac{1}{4}x - 3$, but the right answer is $y = \frac{1}{4}x - 3$.
Here is my solution:
$$x-4y = 12$$
$$x-x-4y = 12-x$$
$$-4y = 12-x $$
$$\frac{-4}{-4}y = -\frac{12}{4}-\frac{x}{4}$$
$$y = -3 - \frac{x}{4} $$
$$y = - \frac{1}{4}x - 3$$

A:

The error is that when dividing both sides by $-4$ you went from $-x$ to $-\frac x4$; it should go to $-\frac{x}{-4}=+\frac{x}{4}$.

