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Question 117320: Hello I really need some help with this math problem it deal with Coordinate Geometry: Linear Equations in Two Variables.
What is the equation of the line that contains the points with (x,y) coordinates (-3,7) and (5,-1) ?
I don't have clue how to set this type of problem up, please help.
thanks
Found 3 solutions by jim_thompson5910, checkley71, Fombitz:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First lets find the slope through the points ( , ) and ( , )
 Start with the slope formula (note: ) is the first point (,) and ) is the second point (,))
 Plug in  , , , (these are the coordinates of given points)
 Subtract the terms in the numerator  to get  . Subtract the terms in the denominator  to get 
 Reduce
So the slope is
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Now let's use the point-slope formula to find the equation of the line:
------Point-Slope Formula------
 where  is the slope, and ) is one of the given points
So lets use the Point-Slope Formula to find the equation of the line
 Plug in , , and (these values are given)
 Rewrite  as 
 Distribute
 Multiply and  to get
 Add to both sides to isolate y
 Combine like terms and to get 
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Answer:
So the equation of the line which goes through the points (,) and (,) is:
The equation is now in  form (which is slope-intercept form) where the slope is and the y-intercept is 
Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver)
 Graph of through the points (,) and (,)
Notice how the two points lie on the line. This graphically verifies our answer.
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! FIRST YOU NEED TO FIND THE SLOPE:
SLOPE=(Y2-Y1)/(X2-X1)
SLOPE=(-1-7)/(5+3)
SLOPE=-8/8
SLOPE=-1
USING THE SLOPE (m) AND A SET OF (X,Y) VALUES IN THE LINE EQUATION Y=mX+b SOLVE FOR (b), THE Y INTERCEPT.
7=-1*-3+b
7=3+b
b=7-3
b=4
THUS THE EQUATION IS:
Y=-X+4
Answer by Fombitz(32388)  (Show Source):
You can put this solution on YOUR website! You need to use the point-slope method of a line.
First calculate the slope, m.
It's the change in y divided by the change in x.
Your points are given as (x,y) pairs.
Your first point is (-3,7).
Your second point is (5,-1).
That means that the change in y is equal to the change in x (all except the negative).
The slope is negative which means as x gets larger, y gets smaller.
You can generate points on your line using this.
Add 1 to x.
Subtract 1 from y.
(-3,7)
(-2,6)
(-1,5)
(0,4)
(1,3)
(2,2)
(3,1)
(4,0)
(5,-1)
Next, use the point slope form of the line.
where m is the slope you just calculated.
( , ) are either of the two points you already know.
 Use the first point (-3,7)
We would have gotten the same answer if we used the second point.
 Use the second point (5,-1)
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