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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.

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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 $x$.

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  • $\begingroup$ Oh, I see what I did wrong. I was trying to get the negative reciprocal and I forgot to make it negative. Dividing it straight out like that works as well, of course (and makes more sense anyway). $\endgroup$ – person27 Oct 11 '13 at 21:58
  • $\begingroup$ @amWhy: Nicely illustrated +1 $\endgroup$ – Amzoti Oct 12 '13 at 13:55

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