SOLUTION: Write the equation of the best-fit line in slope intercept form using the two data point given (9,2)(6,9)

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Question 350960: Write the equation of the best-fit line in slope intercept form using the two data point given (9,2)(6,9)
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
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=9 and y%5B1%5D=2.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=9.


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


m=%289-2%29%2F%286-9%29 Plug in y%5B2%5D=9, y%5B1%5D=2, x%5B2%5D=6, and x%5B1%5D=9


m=%287%29%2F%286-9%29 Subtract 2 from 9 to get 7


m=%287%29%2F%28-3%29 Subtract 9 from 6 to get -3


m=-7%2F3 Reduce


So the slope of the line that goes through the points and is m=-7%2F3


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-2=%28-7%2F3%29%28x-9%29 Plug in m=-7%2F3, x%5B1%5D=9, and y%5B1%5D=2


y-2=%28-7%2F3%29x%2B%28-7%2F3%29%28-9%29 Distribute


y-2=%28-7%2F3%29x%2B21 Multiply


y=%28-7%2F3%29x%2B21%2B2 Add 2 to both sides.


y=%28-7%2F3%29x%2B23 Combine like terms.


So the equation that goes through the points and is y=%28-7%2F3%29x%2B23


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

Also, feel free to check out my tutoring website

Jim