Answer
$y=-\frac{1}{2}x+\frac{13}{2}$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where $m$ = slope and $b$ = y-intercept
(2) Perpendicular lines have slopes whose product is $-1$.
The line we are looking for is perpendicular to the given line $y=2x+1$, whose slope is $2$.
This means that the slope of the line we are looking for has a slope of $-\frac{1}{2}$ since $2(-\frac{1}{2}) = -1$.
Thus, the tentative equation of the line is:
$y =-\frac{1}{2}x+b$
To find the value of $b$, substitute the x and y values of the point $(3, 5)$ to obtain:
$y=-\frac{1}{2}x+b
\\5 = -\frac{1}{2}(3) + b
\\5 = -\frac{3}{2} + b
\\5+\frac{3}{2}=b
\\\frac{10}{2} + \frac{3}{2} = b
\\\frac{13}{2}=b$
Therefore, the equation of the line perpendicular to the given line is:
$y=-\frac{1}{2}x+\frac{13}{2}$
