Question

What's the value of m?

Answer 1

keeping in mind that a perpendicular line to another, will have a negative reciprocal slope, hmmmmm so what's the slope of the equation above anyway?

$\bf y=16-\cfrac{x}{3}\implies \stackrel{\textit{slope-intercept form}}{y = -\cfrac{x}{3}+16}\implies y=\stackrel{slope}{-\cfrac{1}{3}}x+16 \\\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{3}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{3}{1}}\implies 3}$

Answer 2

$k:\ y=m_1x+b\\\\l:\ y=m_2x+c\\\\l\ \perp\ k\ \iff m_1m_2=-1\\\\\text{We have:}\\k:\ y=16-\dfrac{x}{3}=-\dfrac{x}{3}+16=-\dfrac{1}{3}x+16\to m_1=-\dfrac{1}{3}\\\\l:\ y=m_2x+c\\\\l\ \perp\ k\iff-\dfrac{1}{3}m_2=-1\ \ \ \ |\cdot(-3)\\\\m_2=3$

Answer: The value of m is 3.