SOLUTION: What is the equation of the line that passes through the points (-1,5) and (2,-4)

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Question 701788: What is the equation of the line that passes through the points (-1,5) and (2,-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=-1 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=2 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=%28-4-5%29%2F%282--1%29 Plug in y%5B2%5D=-4, y%5B1%5D=5, x%5B2%5D=2, and x%5B1%5D=-1


m=%28-9%29%2F%282--1%29 Subtract 5 from -4 to get -9


m=%28-9%29%2F%283%29 Subtract -1 from 2 to get 3


m=-3 Reduce


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


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


y-5=-3%28x%2B1%29 Rewrite x--1 as x%2B1


y-5=-3x%2B-3%281%29 Distribute


y-5=-3x-3 Multiply


y=-3x-3%2B5 Add 5 to both sides.


y=-3x%2B2 Combine like terms.


So the equation that goes through the points and is y=-3x%2B2