Question

What's the value of m?

Answer 1

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

Answer: The value of m is 3.

Answer 2

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}`