I think I can help you with this. I don't know how much you know already so I'll explain each step.
Lets call the line that contains (4,-9), line 1 and let's call the line that is parallel to this, line 2
Because the two lines are parallel this means they both have the same slope. So if we find the slope of line 2 then we then know the slope of line 1.
So lets look at line 2 which contains (-4, 8) and (8,-1). We use these points in the slope formula,
m=(y2-y1)/(x2-x1). [m is used to represent slope]
Remember that a point is usually in the form (x,y).
In this case, because there are 2 points we need to tell the difference between the two x's and the two y's so we label them (x1,y1) and (x2,y2). ,
[When I'm working a problem, I usually write the label for each number, x1, y1, x2, y2, above it to keep from getting mixed up.]
In this case x1 is -4, y1 is 8, x2 is 8, and y2 is -1.
Plug those in to the formula and solve for m.
[note that I put the negative numbers inside of parenthesis to keep from getting confused]
Remember your order of operation and do any addition or subtraction first.
8-(-4) becomes 8+4 and 8+4=12
We keep this answer as a fraction but reduce the fraction.
9 and 12 are both divisible by 3.
so m= -3/4
This is our slope for both line 1 and line 2
We can now use the Point/Slope Formula to find the equation of the line for line 1
y-y1= m (x-x1)
In this case the (x1, y1) is refering to the point that line 1 contains and m is the slope we just found.
x1 is 4 and y1 is -9
y-y1 = m (x-x1) becomes
simplify and foil
y+9 = -3/4x - (-3/4)(4) becomes
y+9 = -3/4x - (-3) becomes
y+9 = -3/4x+3
subtract 9 from both sides
y = -3/4x-6
You have now found the slope intercept form of the equation of the line y=mx+b.
[so called because we can easily use it to find both the slope m and the y-intercept (0,b)]
I hope that answers your question.