SOLUTION: Which is the equation to the line passing through points (2, –7) and (5, –1)?

Algebra ->  Linear-equations -> SOLUTION: Which is the equation to the line passing through points (2, –7) and (5, –1)?      Log On


   

Question 556313: Which is the equation to the line passing through points (2, –7) 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


Note: is the first point . So this means that x%5B1%5D=2 and y%5B1%5D=-7.
Also, is the second point . So this means that x%5B2%5D=5 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=%28-1--7%29%2F%285-2%29 Plug in y%5B2%5D=-1, y%5B1%5D=-7, x%5B2%5D=5, and x%5B1%5D=2


m=%286%29%2F%285-2%29 Subtract -7 from -1 to get 6


m=%286%29%2F%283%29 Subtract 2 from 5 to get 3


m=2 Reduce


So the slope of the line that goes through the points and is m=2


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--7=2%28x-2%29 Plug in m=2, x%5B1%5D=2, and y%5B1%5D=-7


y%2B7=2%28x-2%29 Rewrite y--7 as y%2B7


y%2B7=2x%2B2%28-2%29 Distribute


y%2B7=2x-4 Multiply


y=2x-4-7 Subtract 7 from both sides.


y=2x-11 Combine like terms.


So the equation that goes through the points and is y=2x-11

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Jim