SOLUTION: What is the equation of the line that goes through the points (4,-1) and (2,3)

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Question 1023989: What is the equation of the line that goes through the points (4,-1) and (2,3)
Answer by MathLover1(20849) 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,-1) and (2,3)


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


m=%283--1%29%2F%282-4%29 Plug in y%5B2%5D=3,y%5B1%5D=-1,x%5B2%5D=2,x%5B1%5D=4 (these are the coordinates of given points)


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




m=-2 Reduce



So the slope is

m=-2





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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--1=%28-2%29%28x-4%29 Plug in m=-2, x%5B1%5D=4, and y%5B1%5D=-1 (these values are given)



y%2B1=%28-2%29%28x-4%29 Rewrite y--1 as y%2B1



y%2B1=-2x%2B%28-2%29%28-4%29 Distribute -2


y%2B1=-2x%2B8 Multiply -2 and -4 to get 8%2F1. Now reduce 8%2F1 to get 8

y=-2x%2B8-1 Subtract 1 from both sides to isolate y


y=-2x%2B7 Combine like terms 8 and -1 to get 7

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Answer:



So the equation of the line which goes through the points (4,-1) and (2,3) is:y=-2x%2B7


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-2 and the y-intercept is b=7


Notice if we graph the equation y=-2x%2B7 and plot the points (4,-1) and (2,3), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-2x%2B7 through the points (4,-1) and (2,3)


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