Answer
$y = 6x$ and $y = 6x-2$ are parallel to each other.
$y=-\frac{1}{6}x$ is perpendicular to both $y = 6x$ and $y = 6x-2$.
Work Step by Step
For two lines to be parallel to each other, their slopes must be equal.
On comparing the equation $y = 6x$ and $y = 6x-2$ with the general equation of line, ie $y=mx+c$ where
$m=$ slope of line
$c=$ intercept on y-axis,
we find that the slope for line $y = 6x$ and $y = 6x-2$ is 6. Therefore the two lines are parallel.
For lines to be perpendicular, their slopes should satisfy the following condition,
$m_{1}\times m_{2} = -1$ (product of slopes should be -1)
Slope for line $y=-\frac{1}{6}x$ is $-\frac{1}{6}$ and for the lines $y = 6x$ and $y = 6x-2$ is 6.
$6 \times -\frac{1}{6}=-1$
Therefore, $y=-\frac{1}{6}x$ is perpendicular to both the lines $y = 6x$ and $y = 6x-2$.
