CPhill, I think you misinterpreted the second equation of a line. :)
You had
$$y=\frac{1}{4}x-3$$
but it looks like it is really
$$y=-\frac{1}{4}x-3$$
In this case, the second line would be going in the opposite direction, and would look something like this: https://www.desmos.com/calculator/fkwxfhm3gd