Find the equation of the line perpendicular to $LaTeX: \displaystyle y = \frac{x}{3} + 3$ that contains $LaTeX: \displaystyle \left( 8, \ 3\right)$ .

The slope of the line is $LaTeX: \displaystyle m = \frac{1}{3}$ so the perpendicular line has slope $LaTeX: \displaystyle m=-3$ . The equation has the form $LaTeX: \displaystyle y=-3x+b$ . Using the point $LaTeX: \displaystyle \left( 8, \ 3\right)$ gives the equation $LaTeX: \displaystyle 3=-3\left(8\right)+b$ Solving for $LaTeX: \displaystyle b$ gives $LaTeX: \displaystyle b = 27$ . The equation of the perpendicular line is $LaTeX: \displaystyle y = 27 - 3 x$ .