SOLUTION: write the equation of the line passing through (8.-4) and (4,6)

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Question 84502: write the equation of the line passing through (8.-4) and (4,6)
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 (8,-4) and (4,6)


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 (8,-4) and (x%5B2%5D,y%5B2%5D) is the second point (4,6))


m=%286--4%29%2F%284-8%29 Plug in y%5B2%5D=6,y%5B1%5D=-4,x%5B2%5D=4,x%5B1%5D=8 (these are the coordinates of given points)


m=+10%2F-4 Subtract the terms in the numerator 6--4 to get 10. Subtract the terms in the denominator 4-8 to get -4




m=-5%2F2 Reduce



So the slope is

m=-5%2F2





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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--4=%28-5%2F2%29%28x-8%29 Plug in m=-5%2F2, x%5B1%5D=8, and y%5B1%5D=-4 (these values are given)



y%2B4=%28-5%2F2%29%28x-8%29 Rewrite y--4 as y%2B4



y%2B4=%28-5%2F2%29x%2B%28-5%2F2%29%28-8%29 Distribute -5%2F2


y%2B4=%28-5%2F2%29x%2B20 Multiply -5%2F2 and -8 to get 40%2F2. Now reduce 40%2F2 to get 20

y=%28-5%2F2%29x%2B20-4 Subtract 4 from both sides to isolate y


y=%28-5%2F2%29x%2B16 Combine like terms 20 and -4 to get 16

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Answer:



So the equation of the line which goes through the points (8,-4) and (4,6) is:y=%28-5%2F2%29x%2B16


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-5%2F2 and the y-intercept is b=16


Notice if we graph the equation y=%28-5%2F2%29x%2B16 and plot the points (8,-4) and (4,6), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-5%2F2%29x%2B16 through the points (8,-4) and (4,6)


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