SOLUTION: write an equation for the line that goes through the points (2,5)and (-1,8)

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Question 595174: write an equation for the line that goes through the points (2,5)and (-1,8)
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=2 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=-1 and y%5B2%5D=8.


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


m=%288-5%29%2F%28-1-2%29 Plug in y%5B2%5D=8, y%5B1%5D=5, x%5B2%5D=-1, and x%5B1%5D=2


m=%283%29%2F%28-1-2%29 Subtract 5 from 8 to get 3


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


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


y-5=-1x%2B-1%28-2%29 Distribute


y-5=-1x%2B2 Multiply


y=-1x%2B2%2B5 Add 5 to both sides.


y=-1x%2B7 Combine like terms.


y=-x%2B7 Simplify


So the equation that goes through the points and is y=-x%2B7


Notice how the graph of y=-x%2B7 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B7 through the points and