SOLUTION: Find the equation of the line satisfying the specified conditions passing thorough (-3,4) and (-5,6)

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Question 929756: Find the equation of the line satisfying the specified conditions
passing thorough (-3,4) and (-5,6)
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=-3 and y%5B1%5D=4.
Also, is the second point . So this means that x%5B2%5D=-5 and y%5B2%5D=6.


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


m=%286-4%29%2F%28-5--3%29 Plug in y%5B2%5D=6, y%5B1%5D=4, x%5B2%5D=-5, and x%5B1%5D=-3


m=%282%29%2F%28-5--3%29 Subtract 4 from 6 to get 2


m=%282%29%2F%28-2%29 Subtract -3 from -5 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-4=-1%28x--3%29 Plug in m=-1, x%5B1%5D=-3, and y%5B1%5D=4


y-4=-1%28x%2B3%29 Rewrite x--3 as x%2B3


y-4=-1x%2B-1%283%29 Distribute


y-4=-1x-3 Multiply


y=-1x-3%2B4 Add 4 to both sides.


y=-1x%2B1 Combine like terms.


y=-x%2B1 Simplify


So the equation that goes through the points and is y=-x%2B1


Notice how the graph of y=-x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B1 through the points and
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