SOLUTION: What is an eqaution of the line that passes through the points (4,-3) and (-4,7)?

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Question 543648: What is an eqaution of the line that passes through the points (4,-3) and (-4,7)?
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=4 and y%5B1%5D=-3.
Also, is the second point . So this means that x%5B2%5D=-4 and y%5B2%5D=7.


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


m=%287--3%29%2F%28-4-4%29 Plug in y%5B2%5D=7, y%5B1%5D=-3, x%5B2%5D=-4, and x%5B1%5D=4


m=%2810%29%2F%28-4-4%29 Subtract -3 from 7 to get 10


m=%2810%29%2F%28-8%29 Subtract 4 from -4 to get -8


m=-5%2F4 Reduce


So the slope of the line that goes through the points and is m=-5%2F4


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--3=%28-5%2F4%29%28x-4%29 Plug in m=-5%2F4, x%5B1%5D=4, and y%5B1%5D=-3


y%2B3=%28-5%2F4%29%28x-4%29 Rewrite y--3 as y%2B3


y%2B3=%28-5%2F4%29x%2B%28-5%2F4%29%28-4%29 Distribute


y%2B3=%28-5%2F4%29x%2B5 Multiply


y=%28-5%2F4%29x%2B5-3 Subtract 3 from both sides.


y=%28-5%2F4%29x%2B2 Combine like terms.


So the equation that goes through the points and is y=%28-5%2F4%29x%2B2


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Jim