SOLUTION: equation through (-5, -1)and (6, -4)

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Question 545347: equation through (-5, -1)and (6, -4)
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=-5 and y%5B1%5D=-1.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=-4.


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


m=%28-4--1%29%2F%286--5%29 Plug in y%5B2%5D=-4, y%5B1%5D=-1, x%5B2%5D=6, and x%5B1%5D=-5


m=%28-3%29%2F%286--5%29 Subtract -1 from -4 to get -3


m=%28-3%29%2F%2811%29 Subtract -5 from 6 to get 11


So the slope of the line that goes through the points and is m=-3%2F11


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=%28-3%2F11%29%28x--5%29 Plug in m=-3%2F11, x%5B1%5D=-5, and y%5B1%5D=-1


y--1=%28-3%2F11%29%28x%2B5%29 Rewrite x--5 as x%2B5


y%2B1=%28-3%2F11%29%28x%2B5%29 Rewrite y--1 as y%2B1


y%2B1=%28-3%2F11%29x%2B%28-3%2F11%29%285%29 Distribute


y%2B1=%28-3%2F11%29x-15%2F11 Multiply


y=%28-3%2F11%29x-15%2F11-1 Subtract 1 from both sides.


y=%28-3%2F11%29x-26%2F11 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=%28-3%2F11%29x-26%2F11