SOLUTION: What is the equation of the line that contains the points with (x,y)coordinates (-3,7)and(5,-1)?

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Question 200448: What is the equation of the line that contains the points with (x,y)coordinates (-3,7)and(5,-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 and is the second point .


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


m=%28-1-7%29%2F%285--3%29 Plug in y%5B2%5D=-1, y%5B1%5D=7, x%5B2%5D=5, and x%5B1%5D=-3


m=%28-8%29%2F%285--3%29 Subtract 7 from -1 to get -8


m=%28-8%29%2F%288%29 Subtract -3 from 5 to get 8


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


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-7=-1%28x--3%29 Plug in m=-1, x%5B1%5D=-3, and y%5B1%5D=7


y-7=-1%28x%2B3%29 Rewrite x--3 as x%2B3


y-7=-1x%2B-1%283%29 Distribute


y-7=-1x-3 Multiply


y=-1x-3%2B7 Add 7 to both sides.


y=-1x%2B4 Combine like terms.


y=-x%2B4 Simplify


So the equation that goes through the points and is y=-x%2B4


Notice how the graph of y=-x%2B4 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B4 through the points and