Answer
Parallel.
Work Step by Step
We know that two parallel lines have the same slope ($m_1=m_2$).
We also know that perpendicular lines have negative reciprocal slopes ($m_1=-\frac{1}{m_2}$).
To calculate the slope between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the formula:
$slope=m=\frac{y_2-y_1}{x_2-x_1}$
We calculate the slope between the points $(15,\ 9)$ and $(12,\ -7)$:
$slope=m=\displaystyle \frac{-7-9}{12-15}=\frac{-16}{-3}=\frac{16}{3}$
Next, we calculate the slope between the points $(8,\ -4)$ and $(5,\ -20)$:
$slope=m=\displaystyle \frac{-20-(-4)}{5-8}=\frac{-16}{-3}=\frac{16}{3}$
We see that the slopes are equal. Thus the lines are parallel.