I'll assume that (6,3) at the end means we want the pependicular through (6,3)
The perpendicular is gotten by swapping the coefficients on x and y and negating one; it doesn't matter which. The point it goes through sets the constant straightforwardly:
6x - 3y = 6(6) - 3(3) = 27
6x - 3y = 27 is the perpendicular