Perpendicular to x + 4y = -4 and through (-4, 4):
Put the equation into slope-intercept form:
4y = -x - 4
y = (-1/4)x - 1
slope = -1/4
Perpendicular lines have negative inverse slopes, so the slope of the desired line is 4.
Using point (-4, 4):
y - 4 = 4(x - (-4))
y - 4 = 4x + 16
y = 4x + 20