Write the equation of the line perpendicular to 3x + y = -8 that passes through (-3, 1). write your answer in slope-intercept form. show work
this is the only question on my quiz i can't get

Slope-intercept form:
y=mx+b
m=slope
b=y-intercept
Any line perpendicular to y=mx+b will have the next slope:
m´=(-1/m)

We have a line:
3x+y=-8
This line in slope-intercept form   (y=mx+b) will be:
y=-3x-8
The slope of this line is : -3

1) we find the slope of any line perpendicular to y=-3x-8
m´=(-1/m)
m´=(-1/-3)=1/3

We have the slope (m=1/3)

2) we find out the equation of the line with m=1/3, and it passes through the point (-3,1).
We have to find "b":
Data:
m=1/3
(-3,1) then when x=-3, y=1

y=mx+b
1=(1/3)(-3)+b
1=-1+b
b=1+1
b=2

Therefore; 
y=mx+b
y=1/3x+2

the equation of the line perpendicular to 3x+y=-8 that passes through (-3,1) is :       y=1/3 x+2