SOLUTION: Find the equation of the line with contains P(-1,3)and Q(1,1)

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Question 215098: Find the equation of the line with contains
P(-1,3)and Q(1,1)
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=-1 and y%5B1%5D=3.
Also, is the second point . So this means that x%5B2%5D=1 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=%281-3%29%2F%281--1%29 Plug in y%5B2%5D=1, y%5B1%5D=3, x%5B2%5D=1, and x%5B1%5D=-1


m=%28-2%29%2F%281--1%29 Subtract 3 from 1 to get -2


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


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


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


y-3=-1x%2B-1%281%29 Distribute


y-3=-1x-1 Multiply


y=-1x-1%2B3 Add 3 to both sides.


y=-1x%2B2 Combine like terms.


y=-x%2B2 Simplify


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


Notice how the graph of y=-x%2B2 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B2 through the points and