Don't use a voltage divider. At least, certainly not for any kind of load that will vary its current draw.
Remember the basic voltage divider equation depends on the same amount of current going through the top resistor as the bottom. So if any current comes in or out of the junction between the resistors, then the voltage won't be what the voltage divider equation said it would be.
A linear regulator like a 7809 will work, but it will dissipate excess energy as heat (a voltage divider would also dissipate heat). The voltage regulator acts like a "smart resistor" that adjusts itself to provide just the right amount of resistance to drop the input voltage to 9V, regardless of the current output, provided you stay within the limits specified on the data sheet.
If your load will draw more than a few milliamps, you'll probably need a heat sink on that regulator. If it will draw more than an amp or so, you're going to need to look into alternate strategies, either a switching regulator or a pass transistor with a massive heat sink.
A buck switching regulator will be more efficient, and therefore won't put out so much heat for large loads. But the 7809 is cheaper and simpler, and would work well for a small load.