SOLUTION: Find a general form equation for the line through the pair of points. (1,4) and (8,-2) I know I am supposed to use the equation Ax + By = C, but I don't know how to plug in

Algebra ->  Equations -> SOLUTION: Find a general form equation for the line through the pair of points. (1,4) and (8,-2) I know I am supposed to use the equation Ax + By = C, but I don't know how to plug in      Log On


   

Question 93118: Find a general form equation for the line through the pair of points.
(1,4) and (8,-2)
I know I am supposed to use the equation Ax + By = C, but I don't know how to plug in for A, B, and C. Please help!! Thanks so much!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (1,4) and (8,-2)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula

m=%28-2-4%29%2F%288-1%29 Plug in y%5B2%5D=-2,y%5B1%5D=4,x%5B2%5D=8,x%5B1%5D=1 (these are the coordinates of given points)

m=+-6%2F7 Subtract the terms in the numerator -2-4 to get -6. Subtract the terms in the denominator 8-1 to get 7

So the slope is
m=-6%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 is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-4=%28-6%2F7%29%28x-1%29 Plug in m=-6%2F7, x%5B1%5D=1, and y%5B1%5D=4 (these values are given)


y-4=%28-6%2F7%29x%2B%28-6%2F7%29%28-1%29 Distribute -6%2F7

y-4=%28-6%2F7%29x%2B6%2F7 Multiply -6%2F7 and -1 to get 6%2F7

y=%28-6%2F7%29x%2B6%2F7%2B4 Add 4 to both sides to isolate y

y=%28-6%2F7%29x%2B34%2F7 Combine like terms 6%2F7 and 4 to get 34%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 (1,4) and (8,-2) is:y=%28-6%2F7%29x%2B34%2F7

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-6%2F7 and the y-intercept is b=34%2F7

Notice if we graph the equation y=%28-6%2F7%29x%2B34%2F7 and plot the points (1,4) and (8,-2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-6%2F7%29x%2B34%2F7 through the points (1,4) and (8,-2)



Now if you want to convert it into standard form then...

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)


y+=+%28-6%2F7%29x%2B34%2F7 Start with the given equation


7%2Ay+=+7%2A%28%28-6%2F7%29x%2B34%2F7%29 Multiply both sides by the LCD 7


7y+=+-6x%2B34 Distribute and multiply


7y%2B6x+=+-6x%2B34%2B6x Add 6x to both sides


6x%2B7y+=+34 Simplify


The original equation y+=+%28-6%2F7%29x%2B34%2F7 (slope-intercept form) is equivalent to 6x%2B7y+=+34 (standard form where A > 0)


The equation 6x%2B7y+=+34 is in the form Ax%2BBy+=+C where A+=+6, B+=+7 and C+=+34