#### 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 $(4,\ 6)$ and $(-8,7)$:
$slope=m=\displaystyle \frac{7-6}{-8-4}=\frac{1}{-12}=-\frac{1}{12}$
Next, we calculate the slope between the points $(-5,5)$ and $(7,\ 4)$:
$slope=m=\displaystyle \frac{4-5}{7-(-5)}=\frac{-1}{12}=-\frac{1}{12}$
We see that the slopes are equal. Thus the lines are parallel.