Answer
Parallel.
Work Step by Step
We know that two parallel lines have the same slope ($m_1=m_2$).
We also know that perpendicular lines have negative reciprocal slopes ($m_1=-\frac{1}{m_2}$).
A line in slope-intercept form has the equation:
$y=mx+b$ ($m=slope$, $b=y-intercept$)
We put the line equations into slope-intercept form:
$3x=y$
$y=3x+0$
$2y-6x=5$
$2y=6x+5$
$y=3x+5/2$
The two slopes ($3$ and $3$) are equal. Thus the lines are parallel.