SOLUTION: write en equation for a slope intercept form that passes through (2,-6) and (1,3)

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Question 87097: write en equation for a slope intercept form that passes through (2,-6) and (1,3)
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 (2,-6) and (1,3)


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 (2,-6) and (x%5B2%5D,y%5B2%5D) is the second point (1,3))


m=%283--6%29%2F%281-2%29 Plug in y%5B2%5D=3,y%5B1%5D=-6,x%5B2%5D=1,x%5B1%5D=2 (these are the coordinates of given points)


m=+9%2F-1 Subtract the terms in the numerator 3--6 to get 9. Subtract the terms in the denominator 1-2 to get -1




m=-9 Reduce



So the slope is

m=-9





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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--6=%28-9%29%28x-2%29 Plug in m=-9, x%5B1%5D=2, and y%5B1%5D=-6 (these values are given)



y%2B6=%28-9%29%28x-2%29 Rewrite y--6 as y%2B6



y%2B6=-9x%2B%28-9%29%28-2%29 Distribute -9


y%2B6=-9x%2B18 Multiply -9 and -2 to get 18%2F1. Now reduce 18%2F1 to get 18

y=-9x%2B18-6 Subtract 6 from both sides to isolate y


y=-9x%2B12 Combine like terms 18 and -6 to get 12

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Answer:



So the equation of the line which goes through the points (2,-6) and (1,3) is:y=-9x%2B12


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-9 and the y-intercept is b=12


Notice if we graph the equation y=-9x%2B12 and plot the points (2,-6) and (1,3), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-9x%2B12 through the points (2,-6) and (1,3)


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