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A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (4,-7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

 Aug 12, 2024
 #1
avatar+37159 
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First, find the slope between the two points:

slope     M = (y1-y2) / (x1-x2)   = (2 - -7 ) /(-8-4) =  - 9 / 12 = - 3/4 

Now the line in y = Mx + b form becomes 

                      Y = -3/4 x + b     Sub in either point to find 'b'  = -4 

then the line equation is    Y = =-3/4 x - 4     

     Re-arrange to 

          3/4 x   + y = -4       Multiply thru by 4 

            3x  + 4y = -16      Done .

 Aug 12, 2024

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