Answer
The two lines are not perpendicular with each other because the slopes are not negative reciprocals of each other..
Work Step by Step
We know that perpendicular lines have slopes that are negative reciprocals of each other. The first thing we want to do would be to find the slopes of both lines.
The slope-intercept form of a line can be given by the equation:
$y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
Since the first equation is already in slope-intercept form, we can see that the slope
for this line is $-2$.
Write the second equation i slope-intercept form to obtain:
$x+2y=8\\
2y = -x + 8\\
y=\frac{-x+8}{2}\\
y=-\frac{x}{2}+4$
We can see that the slope for this line is $-\frac{1}{2}$.
Are $-2$ (slope for the first equation) and $-\frac{1}{2}$ (slope for the second equation) negative reciprocals of one another?
Let us check by multiplying the two slopes together to see if we get $-1$ in return.
$$(-2)\left(-\frac{1}{2}\right) = 1$$
The two lines are NOT perpendicular with each other because the slopes are not negative reciprocals of each other.
