SOLUTION: Which is an equation for the line that contains the points(-2,3)and(2,-1)?

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Question 122562: Which is an equation for the line that contains the points(-2,3)and(2,-1)?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (-2,3) and (2,-1)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (-2,3) and is the second point (2,-1))

m=%28-1-3%29%2F%282--2%29 Plug in y%5B2%5D=-1,y%5B1%5D=3,x%5B2%5D=2,x%5B1%5D=-2 (these are the coordinates of given points)

m=+-4%2F4 Subtract the terms in the numerator -1-3 to get -4. Subtract the terms in the denominator 2--2 to get 4


m=-1 Reduce

So the slope is
m=-1

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-3=%28-1%29%28x--2%29 Plug in m=-1, x%5B1%5D=-2, and y%5B1%5D=3 (these values are given)


y-3=%28-1%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-3=-x%2B%28-1%29%282%29 Distribute -1

y-3=-x-2 Multiply -1 and 2 to get -2

y=-x-2%2B3 Add 3 to both sides to isolate y

y=-x%2B1 Combine like terms -2 and 3 to get 1
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Answer:


So the equation of the line which goes through the points (-2,3) and (2,-1) is:y=-x%2B1

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1 and the y-intercept is b=1

Notice if we graph the equation y=-x%2B1 and plot the points (-2,3) and (2,-1), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-x%2B1 through the points (-2,3) and (2,-1)

Notice how the two points lie on the line. This graphically verifies our answer.