Perpendicular line intersection issues Do not downvote questions for being 'simple' to you.  What one might find trivial another may find helpful.  It is not in the spirit of SE.  That being said,...
I have a line with the equation $y = -2.08x - 44$, and I must find the perpendicular equation, which will be $y \approx 0.4808x - b$.
Using the given coordinates $(0,0)$ for the $\perp$ line, I get $b = 0$.  Now I can set the two lines equal to each other to solve for y, since the y values must be the same at an intersection: $-2.08x - 44 = 0.4808x$.  I get $-2.5608x = 44$, and I can then multiply both sides by (1 / -2.5608) = -0.3905 to get $x = 112.676$.  I then insert that back into the first equation to get $y = -2.08 * 112.676 - 44 = -278.36608$, so that I have $(112.676,278.367)$ which is not the correct answer, since an online calculator states that they intersect at $(-17, -8)$.
My question is, where in this process am I mistaken?  Please tell me so that I can correct my errors and understand where I went wrong.

Up to this point, you are correct: $\require{cancel}$
$$-2.5608\;x = 44$$
Dividing both sides of the equation by $-2.5608$ to solve for $x$ yields (or multiplying both sides by $\frac{1}{-2.5608}$) $$\dfrac{\cancel{-2.5608}\;x}{\cancel{-2.5608}} = \dfrac{44}{-2.5608} \iff x \approx \dfrac {44}{-2.5608} \approx -17.1821$$
Then proceed using the same logic you used to find $y$, but this time, use the correct value for $x$.
