Write an equation for the line parallel to the line −x−8y=3 −x−8y=3 through the point (−1,4)

Parallel means "same slope" so the first thing needed to solve is to find the slope of -x - 8y = 3.  The easiest way to do this is to put it into slope-intercept form (y = mx + b).

- x - 8y = 3
     - 8y = x + 3        Add "x" to both sides
         y = + 3       Divide both sides by "-8"
Slope =

Next, input the slope and point into the point-slope form (y - y1 = m(x - x1))

y - 4 = (x + 1)
y - 4 = -
y      = - + 4
y      = +

The correct one is c.