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find an equation of the line that contains (4,-9) and is parallel to the line that contains (-4,8) and (8,-1)

slope not provided need an equation form

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Peter H. | Tutoring in Math, Science, and Computer EngineeringTutoring in Math, Science, and Computer ...
Hi Mary,
Lines that are parallel have the same slope. Therefore, we need to determine the slope, "m", for the line that contains (-4,8) and (8,-1). The equation for this is
   m = (y1 - y2) / (x1 - x2), where "1" and "2" are our two given points.
Therefore, we have
   m = (8 - -1) / (-4 - 8) = 9/-12 = -3/4
Now that we have "m", we can look at several other posts that take it from there. For example
are a couple of fine answers. So I'll let you take it from here.
Good luck !
Debra A. | Skilled Tutoring in a Variety of Subjects, Personalized to Your NeedsSkilled Tutoring in a Variety of Subject...
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=(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, y1x2, 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.
m=(y2-y1)/(x2-x1) becomes
[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
m=((-1)-8)/(8-(-4)) becomes
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)=(-3/4)(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.