Question

Find the equation of the line that passes through the point (7,5) and is perpendicular to the line 2x - 3y=6

Answer 1

Let line m passes through the point (7,5) and be perpendicular to the line 2x - 3y =6

Let AB be the line having equation 2x - 3y = 6

Therefore, slope of line AB = -a/b               .......Formula

                   Slope               = -2/-3  = 2/3

Therefore, slope of line m = -1/ 2/3  = -3/2

By using Slope-Point form of the line, equation of the line m is,

     y - y1 = m (x - x1)

     y - 5   = -3/2 (x - 7)

   2(y - 5)  = -3 ( x - 7)

  2y  - 10  = -3x + 21

   3x + 2y = 31

Therefore, equation of the line is 3x + 2y + 31