First fine the equation of the line that pass through A and B which is y=Mx+c
The next part, If the line is perpendicular to L means that the gradient of the perpendicular multiply the gradient of L it should be -1 hence we use that formula to find the gradient of the perpendicular line which is -1/3 the question ask for a possible equation but I wrote two to give you a clearer view that there can be two equation of line that is perpendicular to L one is line that is perpendicular at A and one is perpendicular at B