I babysit a fair amount (all through high school and I still do) and as a college student I will not babysit for less than $12 an hour (I have my own car, I'm an EMT/Firefighter, I actually play with the kids...)
After babysitting for many many families over the years, it's not always the money but how good are the kids?? Be honest with yourself. If you know that they will probably give the babysitter a hard time with anything, if the siblings bicker constantly, if they fight, if they will lock themselves in the bathroom, scream and cry for two hours after you leave etc. PLEASE increase the rate per hour.
Another suggestion is pay more for when the kids are awake and then drop the rate a little- I babysit for a 2 and 6 year old and the parents stay out VERY (like 2-3am) late. While the (great) kids are awake I get $12, after they go to sleep at 9pm I get $10. Just another suggestion.