SOLUTION: find an equation of the line containing the given pair of points (4,1) and (12,7) thank you

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Question 395381: find an equation of the line containing the given pair of points
(4,1) and (12,7)
thank you
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=4 and y%5B1%5D=1.
Also, is the second point . So this means that x%5B2%5D=12 and y%5B2%5D=7.


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


m=%287-1%29%2F%2812-4%29 Plug in y%5B2%5D=7, y%5B1%5D=1, x%5B2%5D=12, and x%5B1%5D=4


m=%286%29%2F%2812-4%29 Subtract 1 from 7 to get 6


m=%286%29%2F%288%29 Subtract 4 from 12 to get 8


m=3%2F4 Reduce


So the slope of the line that goes through the points and is m=3%2F4


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-1=%283%2F4%29%28x-4%29 Plug in m=3%2F4, x%5B1%5D=4, and y%5B1%5D=1


y-1=%283%2F4%29x%2B%283%2F4%29%28-4%29 Distribute


y-1=%283%2F4%29x-3 Multiply


y=%283%2F4%29x-3%2B1 Add 1 to both sides.


y=%283%2F4%29x-2 Combine like terms.


So the equation that goes through the points and is y=%283%2F4%29x-2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim