Give the slope-intercept form of the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(–8, –2).
a.
y + 2 = −2(x + 8)
c.
y = −2x − 12
b.
y = −2x − 18
d.
y + 8 = −2(x + 2)

Here, Equation: 2x - 4y = 17
4y = 2x - 17
Divide equation by 4, 
y = 1/2 x - 17/4

Slope = 1/2
So, perpendicular line slope = -2  [ Opposite and reciprocal ]

Now, y - y1 = m(x - x1)
y + 2 = -2(x + 8)
y + 2 = -2x - 16
y = -2x - 18

In short, Your Answer would be Option C

Hope this helps!

Slope intercept is y=mx+b
m=slope
b=y intercept

given

2x-4y=17
slope=-2/-4=1/2
perpendicular lines have sloes that multipy to -1

1/2 times what=-1
times 2 both sides
what=-2

a point is (-8,-2)
in form
y-y1=m(x-x1)
a point is (x1,y1) and sloe is m
y-(-2)=-2(x-(-8))
y+2=-2(x+8)
y+2=-2x-16
minus 2
y=-2x-18

3rd option
why are they mixed up