SOLUTION: What is the equation of a line containing points (-1,2) and (5,-1)

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Question 383185: What is the equation of a line containing points (-1,2) and (5,-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


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


m=%28-1-2%29%2F%285--1%29 Plug in y%5B2%5D=-1, y%5B1%5D=2, x%5B2%5D=5, and x%5B1%5D=-1


m=%28-3%29%2F%285--1%29 Subtract 2 from -1 to get -3


m=%28-3%29%2F%286%29 Subtract -1 from 5 to get 6


m=-1%2F2 Reduce


So the slope of the line that goes through the points and is m=-1%2F2


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-2=%28-1%2F2%29%28x--1%29 Plug in m=-1%2F2, x%5B1%5D=-1, and y%5B1%5D=2


y-2=%28-1%2F2%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-2=%28-1%2F2%29x%2B%28-1%2F2%29%281%29 Distribute


y-2=%28-1%2F2%29x-1%2F2 Multiply


y=%28-1%2F2%29x-1%2F2%2B2 Add 2 to both sides.


y=%28-1%2F2%29x%2B3%2F2 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%2F2%29x%2B3%2F2