SOLUTION: write the equation of the best-fit line in slope intercept form using the two data points given (-5,6)(0,-2)

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Question 350954: write the equation of the best-fit line in slope intercept form using the two data points given (-5,6)(0,-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=-5 and y%5B1%5D=6.
Also, is the second point . So this means that x%5B2%5D=0 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=%28-2-6%29%2F%280--5%29 Plug in y%5B2%5D=-2, y%5B1%5D=6, x%5B2%5D=0, and x%5B1%5D=-5


m=%28-8%29%2F%280--5%29 Subtract 6 from -2 to get -8


m=%28-8%29%2F%285%29 Subtract -5 from 0 to get 5


So the slope of the line that goes through the points and is m=-8%2F5


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=%28-8%2F5%29%28x--5%29 Plug in m=-8%2F5, x%5B1%5D=-5, and y%5B1%5D=6


y-6=%28-8%2F5%29%28x%2B5%29 Rewrite x--5 as x%2B5


y-6=%28-8%2F5%29x%2B%28-8%2F5%29%285%29 Distribute


y-6=%28-8%2F5%29x-8 Multiply


y=%28-8%2F5%29x-8%2B6 Add 6 to both sides.


y=%28-8%2F5%29x-2 Combine like terms.


So the equation that goes through the points and is y=%28-8%2F5%29x-2


Notice how the graph of y=%28-8%2F5%29x-2 goes through the points and . So this visually verifies our answer.
Graph of y=%28-8%2F5%29x-2 through the points and


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

Also, feel free to check out my tutoring website

Jim