Answer
neither
Work Step by Step
Using the properties of equality, the first equation, $
x-2y=6
,$ is equivalent to
\begin{array}{l}
-2y=-x+6
\\\\
y=\dfrac{-1}{-2}x+\dfrac{6}{-2}
\\\\
y=\dfrac{1}{2}x-3
.\end{array}
Using $y=mx+b$, where $m$ is the slope, the slope is
\begin{array}{l}
m_1=\dfrac{1}{2}
.\end{array}
Using the properties of equality, the second equation, $
4x+y=8
,$ is equivalent to
\begin{array}{l}
y=-4x+8
.\end{array}
Using $y=mx+b$, where $m$ is the slope, the slope is
\begin{array}{l}
m_2=-4
.\end{array}
Since $m_1\ne m_2,$ and $m_1\cdot m_2\ne-1$ then the given lines are $\text{
neither parallel nor perpendicular
.}$
