SOLUTION: What is the equation of the line that includes the points (3,6) and (-1,-6)? y=3x-3 y=(3/4)x+5 y=4x+1 y=2x+3/4

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Question 87190: What is the equation of the line that includes the points (3,6) and (-1,-6)?
y=3x-3
y=(3/4)x+5
y=4x+1
y=2x+3/4
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 (3,6) and (-1,-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 (3,6) and (x%5B2%5D,y%5B2%5D) is the second point (-1,-6))


m=%28-6-6%29%2F%28-1-3%29 Plug in y%5B2%5D=-6,y%5B1%5D=6,x%5B2%5D=-1,x%5B1%5D=3 (these are the coordinates of given points)


m=+-12%2F-4 Subtract the terms in the numerator -6-6 to get -12. Subtract the terms in the denominator -1-3 to get -4




m=3 Reduce



So the slope is

m=3





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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=%283%29%28x-3%29 Plug in m=3, x%5B1%5D=3, and y%5B1%5D=6 (these values are given)



y-6=3x%2B%283%29%28-3%29 Distribute 3


y-6=3x-9 Multiply 3 and -3 to get -9%2F1. Now reduce -9%2F1 to get -9

y=3x-9%2B6 Add 6 to both sides to isolate y


y=3x-3 Combine like terms -9 and 6 to get -3

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Answer:



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


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=3 and the y-intercept is b=-3


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


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


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




So the first choice y=3x-3 is the answer