Answer
$y=-\frac{1}{2}x+\frac{13}{2}$
See graph.
Work Step by Step
Step 1. Identify the slope of the given line $y=2x+1$, we have $m_1=2$
Step 2. The slope of the line perpendicular to the above, is then $m=-\frac{1}{m_1}=-\frac{1}{2}$
Step 3. With point $(3,5)$, we have $y-5=-\frac{1}{2}(x-3)$ or $y=-\frac{1}{2}x+\frac{13}{2}$
Step 4. See graph.
