SOLUTION: What would the equation of the line be for the points (2,12) and (1,6)

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Question 681927: What would the equation of the line be for the points (2,12) and (1,6)
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=2 and y%5B1%5D=12.
Also, is the second point . So this means that x%5B2%5D=1 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=%286-12%29%2F%281-2%29 Plug in y%5B2%5D=6, y%5B1%5D=12, x%5B2%5D=1, and x%5B1%5D=2


m=%28-6%29%2F%281-2%29 Subtract 12 from 6 to get -6


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


m=6 Reduce


So the slope of the line that goes through the points and is m=6


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-12=6%28x-2%29 Plug in m=6, x%5B1%5D=2, and y%5B1%5D=12


y-12=6x%2B6%28-2%29 Distribute


y-12=6x-12 Multiply


y=6x-12%2B12 Add 12 to both sides.


y=6x%2B0 Combine like terms.


y=6x Remove the trailing zero


So the equation that goes through the points and is y=6x