Answer
The lines are perpendicular to each other.
Work Step by Step
RECALL:
(i) Two lines are parallel if they have (a) equal slopes or (b) undefined slopes.
(ii) Two lines are perpendicular if they have (a) slopes whose product is −1 or (b) if one has a zero slope and the other has an undefined slope.
(iii) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b=y-intercept.
Write both equations in slope-intercept form to have:
Equation 1:
$6y-2x=5
\\6y=2x+5
\\y=\dfrac{2x+5}{6}
\\y=\dfrac{1}{3}x+\dfrac{5}{6}$
Equation 2:
$2y+6x=1
\\2y=-6x+1
\\y=\dfrac{-6x+1}{2}
\\y=-3x+\frac{1}{2}$
Product of slopes:
$\frac{1}{3}\times-3=1$
The lines have slopes whose product is equal to −1.
Thus, the lines are perpendicular to each other.
