SOLUTION: Find the equation of the line through the points (3,-5) and (-2,-4)

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Question 228712: Find the equation of the line through the points (3,-5) and (-2,-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,-5) and (-2,-4)


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


m=%28-4--5%29%2F%28-2-3%29 Plug in y%5B2%5D=-4,y%5B1%5D=-5,x%5B2%5D=-2,x%5B1%5D=3 (these are the coordinates of given points)


m=+1%2F-5 Subtract the terms in the numerator -4--5 to get 1. Subtract the terms in the denominator -2-3 to get -5




m=-1%2F5 Reduce



So the slope is

m=-1%2F5





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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--5=%28-1%2F5%29%28x-3%29 Plug in m=-1%2F5, x%5B1%5D=3, and y%5B1%5D=-5 (these values are given)



y%2B5=%28-1%2F5%29%28x-3%29 Rewrite y--5 as y%2B5



y%2B5=%28-1%2F5%29x%2B%28-1%2F5%29%28-3%29 Distribute -1%2F5


y%2B5=%28-1%2F5%29x%2B3%2F5 Multiply -1%2F5 and -3 to get 3%2F5

y=%28-1%2F5%29x%2B3%2F5-5 Subtract 5 from both sides to isolate y


y=%28-1%2F5%29x-22%2F5 Combine like terms 3%2F5 and -5 to get -22%2F5 (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 (3,-5) and (-2,-4) is:y=%28-1%2F5%29x-22%2F5


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F5 and the y-intercept is b=-22%2F5


Notice if we graph the equation y=%28-1%2F5%29x-22%2F5 and plot the points (3,-5) and (-2,-4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F5%29x-22%2F5 through the points (3,-5) and (-2,-4)


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