Answer
$y=-\dfrac{1}{2}x+\dfrac{13}{2}$
Work Step by Step
We are given the line:
$y=2x+1$
Let $y=mx+b$ be the equation of the line we are looking for. The slope of the line $y=2x+1$ is 2. Because the two lines are perpendicular, we have:
$m\cdot 2=-1$
Determine $m$:
$m=-\dfrac{1}{2}$
We determine the equation of the line using the slope $m$ and the point $(3,5)$:
$y-5=-\dfrac{1}{2}(x-3)$
Put the equation in slope-intercept form:
$y=-\dfrac{1}{2}x+\dfrac{3}{2}+5$
$y=-\dfrac{1}{2}x+\dfrac{13}{2}$
Use the points $(3,5)$ and $\left(0,\dfrac{13}{2}\right)$ to graph the line:
