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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)

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2 Answers

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 !
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.