Perpendicular lines have opposite reciprocals from the original line.
Original line: y=-3/4x+6
Perpendicular line: y=4/3x+b
Solve for b by plugging in the given coordinates (3,9) for x and y respectively.
9=4/3(3)+b
Multiply 4/3*3.
9=4+b
Subtract 4 from both sides.
5=b
Now, with b and the slope, you can write the equation:
y=4/3x+5
I hope this helps :)