Equation perpendicular to x+2y=-4 with a point of (-8,5)

The equation is there so you can find the rate of change and the y-intercept which is done like so:
rearange the variables and numbers by moving the x it the right side of the = which becomes -x.
2y= -x-4
divide the 2 by the -x and -4
which gives us:
y= -1/2x -2
so the rate of change is -1/2 and the y-intercept is -2.
we use the points to plug it into an equation that looks like this:
y-y1 = m(x-x1)

plug in the numbers like so:
y-5= -1/2(x+8)
distribute first:
y-5= -(1/2)x - 4
then get the y alone by adding 5 to -4, which leaves us with
y = -(1/2)x+1

the answer is:
Y= -(1/2)X +1