According to the Texas Department of Public Safety, all children younger than 8 years old, unless taller than 4'9", are required to be in the appropriate child safety seat system wherever they ride in a passenger vehicle. The safety seat system MUST be installed according to the manufacturer's instructions. Another way of saying this is:

When a child reaches their 8th birthday - no matter their height, it is legal for the child to use only the adult safety belt in the passenger vehicle.