SOLUTION: what is the equation of a line given the two points (2,1) (-2,-1)

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Question 626970: what is the equation of a line given the two points (2,1) (-2,-1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=2 and y%5B1%5D=1.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=-1.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-1-1%29%2F%28-2-2%29 Plug in y%5B2%5D=-1, y%5B1%5D=1, x%5B2%5D=-2, and x%5B1%5D=2


m=%28-2%29%2F%28-2-2%29 Subtract 1 from -1 to get -2


m=%28-2%29%2F%28-4%29 Subtract 2 from -2 to get -4


m=1%2F2 Reduce


So the slope of the line that goes through the points and is m=1%2F2


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-1=%281%2F2%29%28x-2%29 Plug in m=1%2F2, x%5B1%5D=2, and y%5B1%5D=1


y-1=%281%2F2%29x%2B%281%2F2%29%28-2%29 Distribute


y-1=%281%2F2%29x-1 Multiply


y=%281%2F2%29x-1%2B1 Add 1 to both sides.


y=%281%2F2%29x%2B0 Combine like terms.


y=%281%2F2%29x Remove the trailing zero


So the equation that goes through the points and is y=%281%2F2%29x


Notice how the graph of y=%281%2F2%29x goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x through the points and


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