SOLUTION: Write the equation of the line Through twompoints (-6,10) and (3,1)

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Question 645776: Write the equation of the line
Through twompoints (-6,10) and (3,1)
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=-6 and y%5B1%5D=10.
Also, is the second point . So this means that x%5B2%5D=3 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=%281-10%29%2F%283--6%29 Plug in y%5B2%5D=1, y%5B1%5D=10, x%5B2%5D=3, and x%5B1%5D=-6


m=%28-9%29%2F%283--6%29 Subtract 10 from 1 to get -9


m=%28-9%29%2F%289%29 Subtract -6 from 3 to get 9


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-10=-1%28x--6%29 Plug in m=-1, x%5B1%5D=-6, and y%5B1%5D=10


y-10=-1%28x%2B6%29 Rewrite x--6 as x%2B6


y-10=-1x%2B-1%286%29 Distribute


y-10=-1x-6 Multiply


y=-1x-6%2B10 Add 10 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


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