SOLUTION: Find the equation of the line containing the points (3,4) and (1,-3)

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Question 110732: Find the equation of the line containing the points (3,4) and (1,-3)
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 (3,4) and (1,-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 (3,4) and (x%5B2%5D,y%5B2%5D) is the second point (1,-3))


m=%28-3-4%29%2F%281-3%29 Plug in y%5B2%5D=-3,y%5B1%5D=4,x%5B2%5D=1,x%5B1%5D=3 (these are the coordinates of given points)


m=+-7%2F-2 Subtract the terms in the numerator -3-4 to get -7. Subtract the terms in the denominator 1-3 to get -2




m=7%2F2 Reduce



So the slope is

m=7%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-4=%287%2F2%29%28x-3%29 Plug in m=7%2F2, x%5B1%5D=3, and y%5B1%5D=4 (these values are given)



y-4=%287%2F2%29x%2B%287%2F2%29%28-3%29 Distribute 7%2F2


y-4=%287%2F2%29x-21%2F2 Multiply 7%2F2 and -3 to get -21%2F2

y=%287%2F2%29x-21%2F2%2B4 Add 4 to both sides to isolate y


y=%287%2F2%29x-13%2F2 Combine like terms -21%2F2 and 4 to get -13%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 (3,4) and (1,-3) is:y=%287%2F2%29x-13%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=7%2F2 and the y-intercept is b=-13%2F2


Notice if we graph the equation y=%287%2F2%29x-13%2F2 and plot the points (3,4) and (1,-3), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%287%2F2%29x-13%2F2 through the points (3,4) and (1,-3)


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