SOLUTION: how do you find the equation for these points {4,-8} {-3,1}

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Question 912766: how do you find the equation for these points {4,-8} {-3,1}
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (4,-8) and (-3,1)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (4,-8) and (x%5B2%5D,y%5B2%5D) is the second point (-3,1))


m=%281--8%29%2F%28-3-4%29 Plug in y%5B2%5D=1,y%5B1%5D=-8,x%5B2%5D=-3,x%5B1%5D=4 (these are the coordinates of given points)


m=+9%2F-7 Subtract the terms in the numerator 1--8 to get 9. Subtract the terms in the denominator -3-4 to get -7




m=-9%2F7 Reduce



So the slope is

m=-9%2F7





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y--8=%28-9%2F7%29%28x-4%29 Plug in m=-9%2F7, x%5B1%5D=4, and y%5B1%5D=-8 (these values are given)



y%2B8=%28-9%2F7%29%28x-4%29 Rewrite y--8 as y%2B8



y%2B8=%28-9%2F7%29x%2B%28-9%2F7%29%28-4%29 Distribute -9%2F7


y%2B8=%28-9%2F7%29x%2B36%2F7 Multiply -9%2F7 and -4 to get 36%2F7

y=%28-9%2F7%29x%2B36%2F7-8 Subtract 8 from both sides to isolate y


y=%28-9%2F7%29x-20%2F7 Combine like terms 36%2F7 and -8 to get -20%2F7 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (4,-8) and (-3,1) is:y=%28-9%2F7%29x-20%2F7


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-9%2F7 and the y-intercept is b=-20%2F7


Notice if we graph the equation y=%28-9%2F7%29x-20%2F7 and plot the points (4,-8) and (-3,1), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-9%2F7%29x-20%2F7 through the points (4,-8) and (-3,1)


Notice how the two points lie on the line. This graphically verifies our answer.





Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim