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A line passes through the points (-3,-5) and (6,1). The equation of this line can be written in the form Ax + By = C, where A, B, and C are integers with greatest common divisor 1, and A is positive.

 Apr 10, 2020
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First:  find the slope:  slope  =  ( y2 - y1 ) / ( x2 - x1 )  =  ( 1 - -5 ) / ( 6 - -3 )  =  6 / 9  =  2/3

 

Then:  use the point-slope form for a straight line:  y - y1  =  m(x - x1)   --->   y - -5  =  (2/3)(x - -3)

          --->   y + 5  =  (2/3)(x + 3)    

          --->  3y + 15  =  2(x + 3)

          --->   3y + 15  =  2x + 6

         --->   -2x + 3y  =  -9

        --->   2x - 3y  =  9

 Apr 10, 2020

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