SOLUTION: What is the equation of the line that passes through the points (5, 2) and (−5, 7)?

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Question 478254: What is the equation of the line that passes through the points (5, 2) and (−5, 7)?
Answer by MathLover1(20850) 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 (-5,7)


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 (-5,7))


m=%287-2%29%2F%28-5-5%29 Plug in y%5B2%5D=7,y%5B1%5D=2,x%5B2%5D=-5,x%5B1%5D=5 (these are the coordinates of given points)


m=+5%2F-10 Subtract the terms in the numerator 7-2 to get 5. Subtract the terms in the denominator -5-5 to get -10




m=-1%2F2 Reduce



So the slope is

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



y-2=%28-1%2F2%29x%2B%28-1%2F2%29%28-5%29 Distribute -1%2F2


y-2=%28-1%2F2%29x%2B5%2F2 Multiply -1%2F2 and -5 to get 5%2F2

y=%28-1%2F2%29x%2B5%2F2%2B2 Add 2 to both sides to isolate y


y=%28-1%2F2%29x%2B9%2F2 Combine like terms 5%2F2 and 2 to get 9%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 (5,2) and (-5,7) is:y=%28-1%2F2%29x%2B9%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F2 and the y-intercept is b=9%2F2


Notice if we graph the equation y=%28-1%2F2%29x%2B9%2F2 and plot the points (5,2) and (-5,7), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F2%29x%2B9%2F2 through the points (5,2) and (-5,7)


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