SOLUTION: What is the equation of line as a solution for the given pair (2,10) and (1,5)

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Question 714887: What is the equation of line as a solution for the given pair (2,10) and (1,5)
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=10.
Also, is the second point . So this means that x%5B2%5D=1 and y%5B2%5D=5.


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


m=%285-10%29%2F%281-2%29 Plug in y%5B2%5D=5, y%5B1%5D=10, x%5B2%5D=1, and x%5B1%5D=2


m=%28-5%29%2F%281-2%29 Subtract 10 from 5 to get -5


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


m=5 Reduce


So the slope of the line that goes through the points and is m=5


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-10=5%28x-2%29 Plug in m=5, x%5B1%5D=2, and y%5B1%5D=10


y-10=5x%2B5%28-2%29 Distribute


y-10=5x-10 Multiply


y=5x-10%2B10 Add 10 to both sides.


y=5x%2B0 Combine like terms.


y=5x Remove the trailing zero


So the equation that goes through the points and is y=5x