Hi Mary,

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=(y_{2}-y_{1})/(x_{2-}x_{1}). [*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 (x_{1},y_{1}) and (x_{2},y_{2}). ,

*[When I'm working a problem, **I usually write the label for each number,* x_{1}, y_{1}, *x*_{2}, y_{2}, above it to keep from getting mixed up.]

In this case x_{1 }is -4, y_{1} is 8, x_{2} is 8, and y_{2} is -1.

Plug those in to the formula and solve for m.

m=(y_{2}-y_{1})/(x_{2}-x_{1}) becomes

m=((-1)-8)/(8-(-4)).

[*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.

(-1)-8=-9

8-(-4) becomes 8+4 and 8+4=12

m=((-1)-8)/(8-(-4)) becomes

m=(-9)/(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-y_{1}= m (x-x_{1})

In this case the (x_{1}, y_{1}) is refering to the point that line 1 contains and m is the slope we just found.

x_{1} is 4 and y_{1} is -9

y-y_{1 }= m (x-x_{1}) becomes

y-(-9)=(-3/4)(x-4)

simplify and foil

y-(-9)=(-3/4)(x-4) becomes

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+9-9=-3/4x+3-9 becomes

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.

Debra A.