#### Answer

The two lines are perpendicular to each other.

#### Work Step by Step

RECALL:
(1) Parallel lines have equal slopes.
(2) Perpendicular lines have slopes whose product is $-1$.
(3) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope.
Write both equations in slope-intercept form to obtain:
$\bf\text{Equation 1}:$
$6y-2x=5
\\6y=2x+5
\\\dfrac{6y}{6} = \dfrac{2x+5}{6}
\\y = \dfrac{2}{6}x + \dfrac{5}{6}
\\y=\dfrac{1}{3}x+\dfrac{5}{6}$
$\bf\text{Equation 2}:$
$2y+6x=1
\\2y=-6x+1
\\\dfrac{2y}{2} = \dfrac{-6x+1}{2}
\\y=-3x+\dfrac{1}{2}$
The two lines have slopes that are negative reciprocals of each other (product is -1).
Thus, the two lines are perpendicular to each other.