Answer
Perpendicular
Work Step by Step
$y=6x-\frac{1}{3}$
$x+6y=6$
$6y=-x+6$
$y=-\frac{1}{6}x+1$
The coefficients of $x$ for both equations are not the same, so the slopes are different. This means this pair of lines is not parallel.
For a pair of lines to be perpendicular to each other, the slope of one equation must be the negative reciprocal of the other. $6$ and $-\frac{1}{6}$ are negative reciprocals of each other. This means this pair of lines is perpendicular.
