Answer
The graphs are not perpendicular.
Work Step by Step
RECALL:
(1) In the slope-intercept form of a line's equation $y=mx+b$, $m$=slope and $b$ is the y-coordinate of the y-intercept.
(2) Perpendicular lines have slopes whose product is $-1$ (or negative reciprocals of each other).
Write both equations in slope-intercept form to obtain:
First Equation:
$y=3x+1$
Second Equation:
$6x+2y=5
\\6x+2y-6x=5-6x
\\2y=5-6x
\\2y=-6x+5
\\\frac{2y}{2}=\frac{-6x+5}{2}
\\y=-3x+\frac{5}{2}$
Note that equations have the slopes $3$ and $-3$.
Since $3 \cdot (-3) \ne -1$, then the graphs of the two equations are NOT perpendicular lines.