SOLUTION: Write the equation of the line given the two points (-2,3) and (1,1)

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Question 109947: Write the equation of the line given the two points (-2,3) and (1,1)
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 (-2,3) and (1,1)


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


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


m=+-2%2F3 Subtract the terms in the numerator 1-3 to get -2. Subtract the terms in the denominator 1--2 to get 3



So the slope is

m=-2%2F3





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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-3=%28-2%2F3%29%28x--2%29 Plug in m=-2%2F3, x%5B1%5D=-2, and y%5B1%5D=3 (these values are given)



y-3=%28-2%2F3%29%28x%2B2%29 Rewrite x--2 as x%2B2



y-3=%28-2%2F3%29x%2B%28-2%2F3%29%282%29 Distribute -2%2F3


y-3=%28-2%2F3%29x-4%2F3 Multiply -2%2F3 and 2 to get -4%2F3

y=%28-2%2F3%29x-4%2F3%2B3 Add 3 to both sides to isolate y


y=%28-2%2F3%29x%2B5%2F3 Combine like terms -4%2F3 and 3 to get 5%2F3 (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 (-2,3) and (1,1) is:y=%28-2%2F3%29x%2B5%2F3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-2%2F3 and the y-intercept is b=5%2F3


Notice if we graph the equation y=%28-2%2F3%29x%2B5%2F3 and plot the points (-2,3) and (1,1), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-2%2F3%29x%2B5%2F3 through the points (-2,3) and (1,1)


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