I want to reduce this equation to the form of y = kx + b, but I cann't do that using MMA.

Collect[(Det[( {
       {1, x, y},
       {1, a, b},
       {1, c, d}
      } )] == 0) // FullSimplify(*Two points determine a straight line*), {x, y}]

I want to reduce this equation to the form of y == kx + b, but I cann't do that using MMA.

Collect[(Det[( {
       {1, x, y},
       {1, a, b},
       {1, c, d}
      } )] == 0) // FullSimplify(*Two points determine a straight line*), {x, y}]