#### Answer

Perpendicular.

#### 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 ($m_1=-\frac{1}{m_2}$).
A line in slope-intercept form has the equation:
$y=mx+b$ ($m=slope$, $b=y-intercept$)
We put the line equations into slope-intercept form:
$x+4y=7$
$4y=-x+7$
$y=(-x+7)/4$
$y=-\frac{1}{4}x+\frac{7}{4}$
$4x-y=3$
$-y=-4x+3$
$y=-(-4x+3)$
$y=4x-3$
The two slopes (-$\displaystyle \frac{1}{4}$ and $4$) are negative reciprocals of each other. Thus the lines are perpendicular.