SOLUTION: Identify the slope of the line passing through the pair of points (5,2) and (−2, 1).

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Question 449033: Identify the slope of the line passing through the pair of points (5,2) and (−2, 1).
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 (5,2) and (-2,1)


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


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


m=+-1%2F-7 Subtract the terms in the numerator 1-2 to get -1. Subtract the terms in the denominator -2-5 to get -7




m=1%2F7 Reduce



So the slope is

m=1%2F7





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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-2=%281%2F7%29%28x-5%29 Plug in m=1%2F7, x%5B1%5D=5, and y%5B1%5D=2 (these values are given)



y-2=%281%2F7%29x%2B%281%2F7%29%28-5%29 Distribute 1%2F7


y-2=%281%2F7%29x-5%2F7 Multiply 1%2F7 and -5 to get -5%2F7

y=%281%2F7%29x-5%2F7%2B2 Add 2 to both sides to isolate y


y=%281%2F7%29x%2B9%2F7 Combine like terms -5%2F7 and 2 to get 9%2F7 (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 (5,2) and (-2,1) is:y=%281%2F7%29x%2B9%2F7


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F7 and the y-intercept is b=9%2F7


Notice if we graph the equation y=%281%2F7%29x%2B9%2F7 and plot the points (5,2) and (-2,1), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F7%29x%2B9%2F7 through the points (5,2) and (-2,1)


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