SOLUTION: What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?

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Question 270218: What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?
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,-1) and (-1,5)


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


m=%285--1%29%2F%28-1-3%29 Plug in y%5B2%5D=5,y%5B1%5D=-1,x%5B2%5D=-1,x%5B1%5D=3 (these are the coordinates of given points)


m=+6%2F-4 Subtract the terms in the numerator 5--1 to get 6. Subtract the terms in the denominator -1-3 to get -4




m=-3%2F2 Reduce



So the slope is

m=-3%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--1=%28-3%2F2%29%28x-3%29 Plug in m=-3%2F2, x%5B1%5D=3, and y%5B1%5D=-1 (these values are given)



y%2B1=%28-3%2F2%29%28x-3%29 Rewrite y--1 as y%2B1



y%2B1=%28-3%2F2%29x%2B%28-3%2F2%29%28-3%29 Distribute -3%2F2


y%2B1=%28-3%2F2%29x%2B9%2F2 Multiply -3%2F2 and -3 to get 9%2F2

y=%28-3%2F2%29x%2B9%2F2-1 Subtract 1 from both sides to isolate y


y=%28-3%2F2%29x%2B7%2F2 Combine like terms 9%2F2 and -1 to get 7%2F2 (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,-1) and (-1,5) is:y=%28-3%2F2%29x%2B7%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-3%2F2 and the y-intercept is b=7%2F2


Notice if we graph the equation y=%28-3%2F2%29x%2B7%2F2 and plot the points (3,-1) and (-1,5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-3%2F2%29x%2B7%2F2 through the points (3,-1) and (-1,5)


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