I need some advice for a first time skiier (9 years old)?

Make your kid watch "how to" and "skiing safety" videos on youtube...they can be very helpful.

Beginner lessons should not put any client on steep slopes. Beginners should be enrolled in a class and for beginners they are usually sliding on very flat snow. The biggest danger there is being hit by other beginners but they are seldom moving faster than a walk. Children fall and get up. They are used to this and if you have watched youth sports like soccer you will see nearly every player on the ground at some time and they get up and go again. Skiing is slippery but seldom dangerous when the instructor is a qualified professional.

Well for one your child will not be in the same group as the adult family member. He will be grouped by age and then by skill. Being a true first timer, he won't be going on any real ski run. It will be a nice gentle slope where they will teach him terms like Pizza, and French Fries and how to turn. At the mountains in Colorado, they give lessons to kids that are 3-4 yo.

he sounds like a cool kid. make him wear a helmet and don't worry, he can't get hurt that bad. Beginners tend to go as fast as they can (not very fast) and then fall and this is natural; however, they cannot remain balanced for very long so they fall at such a slow speed that nothing bad happens. 3-4 more times up on the mountain, he will be in the park (jumps and rails area) where he can get more seriously hurt so worry then. :)

Don't let your ability (or lack there of) keep your child from enjoying skiing. It's good they take a lesson first. Few people get seriously hurt beginning skiing unless they are trying to do something they shouldn't.

Put a helmet on him and don't worry. Kids are naturals at skiing and being smaller than adults they tend to catch on faster and their falls are less traumatic. You acting worried or fussing about him will tend to undermine his confidence and fear is more likely to get him hurt in skiing than relaxed enthusiasm.