SOLUTION: Find the general form of the equation of the line that passes through the points (-1,-2) and (7,1).

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Question 462594: Find the general form of the equation of the line that passes through the points (-1,-2) and (7,1).
Found 2 solutions by MathLover1, stanbon:
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 (-1,-2) and (7,1)


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 (-1,-2) and (x%5B2%5D,y%5B2%5D) is the second point (7,1))


m=%281--2%29%2F%287--1%29 Plug in y%5B2%5D=1,y%5B1%5D=-2,x%5B2%5D=7,x%5B1%5D=-1 (these are the coordinates of given points)


m=+3%2F8 Subtract the terms in the numerator 1--2 to get 3. Subtract the terms in the denominator 7--1 to get 8



So the slope is

m=3%2F8





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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=%283%2F8%29%28x--1%29 Plug in m=3%2F8, x%5B1%5D=-1, and y%5B1%5D=-2 (these values are given)



y%2B2=%283%2F8%29%28x--1%29 Rewrite y--2 as y%2B2



y%2B2=%283%2F8%29%28x%2B1%29 Rewrite x--1 as x%2B1



y%2B2=%283%2F8%29x%2B%283%2F8%29%281%29 Distribute 3%2F8


y%2B2=%283%2F8%29x%2B3%2F8 Multiply 3%2F8 and 1 to get 3%2F8

y=%283%2F8%29x%2B3%2F8-2 Subtract 2 from both sides to isolate y


y=%283%2F8%29x-13%2F8 Combine like terms 3%2F8 and -2 to get -13%2F8 (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 (-1,-2) and (7,1) is:y=%283%2F8%29x-13%2F8


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=3%2F8 and the y-intercept is b=-13%2F8


Notice if we graph the equation y=%283%2F8%29x-13%2F8 and plot the points (-1,-2) and (7,1), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%283%2F8%29x-13%2F8 through the points (-1,-2) and (7,1)


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




so, your line in slope-intercept form is: y=%283%2F8%29x-13%2F8
in the general form of the equation of the line ax+%2B+by+=+c will be:
%283%2F8%29x+%2B+y=-13%2F8

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the general form of the equation of the line that passes through the points (-1,-2) and (7,1).
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slope = (1--2)/(7--1) = 3/8
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Form: y = mx+b
1 = (3/8)7 + b
(8/8) = (21/8) + b
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b = -13/8
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y = (3/8)x-(13/8)
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Cheers,
Stan H.