Question

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 1

Let A = (1,4) = (x1,y1) and B = (8,-2) = (x2,y2)

By using Tow-Point Form of a Line,

   y - y1 / y1 - y2 = x - x1 / x1 - x2

   y - 4 / 4 - (-2)   = x - 1 / 1 - 8

   y - 4 / 4 + 2      = x - 1 / -7

   y -4 / 6             = x - 1 / 7

   7 ( y - 4 )          = 6 ( x - 1 )     .....  Cross multiplication

   7y - 28              = 6x -6

Therefore, 6x - 7y = -28 + 6

                  6x - 7y = -22

Therefore, equation of the line passing through the given points is 6x - 7y = -22