SOLUTION: find the equation for the line through the points (-6,-4) and (2,-5)

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Question 509002: find the equation for the line through the points (-6,-4) and (2,-5)
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=-4.
Also, is the second point . So this means that x%5B2%5D=2 and y%5B2%5D=-5.


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


m=%28-5--4%29%2F%282--6%29 Plug in y%5B2%5D=-5, y%5B1%5D=-4, x%5B2%5D=2, and x%5B1%5D=-6


m=%28-1%29%2F%282--6%29 Subtract -4 from -5 to get -1


m=%28-1%29%2F%288%29 Subtract -6 from 2 to get 8


So the slope of the line that goes through the points and is m=-1%2F8


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--4=%28-1%2F8%29%28x--6%29 Plug in m=-1%2F8, x%5B1%5D=-6, and y%5B1%5D=-4


y--4=%28-1%2F8%29%28x%2B6%29 Rewrite x--6 as x%2B6


y%2B4=%28-1%2F8%29%28x%2B6%29 Rewrite y--4 as y%2B4


y%2B4=%28-1%2F8%29x%2B%28-1%2F8%29%286%29 Distribute


y%2B4=%28-1%2F8%29x-3%2F4 Multiply


y=%28-1%2F8%29x-3%2F4-4 Subtract 4 from both sides.


y=%28-1%2F8%29x-19%2F4 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%28-1%2F8%29x-19%2F4