SOLUTION: Find an equation of the line containing the given par of points (2,4) and (6,5)

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Question 268044: Find an equation of the line containing the given par of points
(2,4) and (6,5)


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 (2,4) and (6,5)


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 (2,4) and (x%5B2%5D,y%5B2%5D) is the second point (6,5))


m=%285-4%29%2F%286-2%29 Plug in y%5B2%5D=5,y%5B1%5D=4,x%5B2%5D=6,x%5B1%5D=2 (these are the coordinates of given points)


m=+1%2F4 Subtract the terms in the numerator 5-4 to get 1. Subtract the terms in the denominator 6-2 to get 4



So the slope is

m=1%2F4





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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=%281%2F4%29%28x-2%29 Plug in m=1%2F4, x%5B1%5D=2, and y%5B1%5D=4 (these values are given)



y-4=%281%2F4%29x%2B%281%2F4%29%28-2%29 Distribute 1%2F4


y-4=%281%2F4%29x-1%2F2 Multiply 1%2F4 and -2 to get -2%2F4. Now reduce -2%2F4 to get -1%2F2

y=%281%2F4%29x-1%2F2%2B4 Add 4 to both sides to isolate y


y=%281%2F4%29x%2B7%2F2 Combine like terms -1%2F2 and 4 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 (2,4) and (6,5) is:y=%281%2F4%29x%2B7%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F4 and the y-intercept is b=7%2F2


Notice if we graph the equation y=%281%2F4%29x%2B7%2F2 and plot the points (2,4) and (6,5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F4%29x%2B7%2F2 through the points (2,4) and (6,5)


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