SOLUTION: Write the equation of the best-fit line in slope intercept form using the two data point given (1,6)(-1,2)

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the best-fit line in slope intercept form using the two data point given (1,6)(-1,2)      Log On


   

Question 350964: Write the equation of the best-fit line in slope intercept form using the two data point given (1,6)(-1,2)
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=1 and y%5B1%5D=6.
Also, is the second point . So this means that x%5B2%5D=-1 and y%5B2%5D=2.


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


m=%282-6%29%2F%28-1-1%29 Plug in y%5B2%5D=2, y%5B1%5D=6, x%5B2%5D=-1, and x%5B1%5D=1


m=%28-4%29%2F%28-1-1%29 Subtract 6 from 2 to get -4


m=%28-4%29%2F%28-2%29 Subtract 1 from -1 to get -2


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-6=2%28x-1%29 Plug in m=2, x%5B1%5D=1, and y%5B1%5D=6


y-6=2x%2B2%28-1%29 Distribute


y-6=2x-2 Multiply


y=2x-2%2B6 Add 6 to both sides.


y=2x%2B4 Combine like terms.


So the equation that goes through the points and is y=2x%2B4


Notice how the graph of y=2x%2B4 goes through the points and . So this visually verifies our answer.
Graph of y=2x%2B4 through the points and

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Jim