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 line perpendicular to it will have a slope $m=-\frac{1}{m_1}=-\frac{2}{3}$
Step 3. With point $(1,5)$, we can write the equation as $y-5=-\frac{2}{3}(x-1)$ or $y=-\frac{2}{3}x+\frac{17}{3}$
