Hi, I am stuck on a geometry problem and it's really frustrating, it concerns the proof to the theorem that says "If two nonvertical lines are perpendicular, the product of their slopes is -1."

Now, this might be considered an algebra problem, but in the exercise I have to find the answer to:

Please let me know if I need to include more information or anything if this seems vague, it's probably an easy problem but I just don't understand how to get the correct answer, thanks.