Answer
$y=-\frac{2}{3}x+\frac{17}{3}$
Work Step by Step
Step 1. Find the slope of the given line as $m_1=\frac{3}{2}$.
Step 2. The new line perpendicular to the above will have a slope $m=-\frac{1}{m_1}=-\frac{2}{3}$.
Step 3. With point $(1,5)$, we have $y-5=-\frac{2}{3}(x-1)$ or $y=-\frac{2}{3}x+\frac{17}{3}$
