Rep. Allen Vaught, a Dallas Democrat who sponsored the bill, said seat belts do not fit children properly and can injure or kill them in an accident.
Starting in June 2010, people who don't follow the law would face a $25 fine, which would be used to buy booster seats for low-income families. Until then, police officers would only issue warnings. Subsequent violations could result in fines up to $250.
Experts say children between 4 and 8 who are using adult restraints are likely to suffer severe head, spinal cord and internal injuries during accidents and that booster seats can reduce that risk of injury by more than 50 percent.
Some conservative Republicans from the Houston area raised opposition to the bill, arguing that it would be difficult for parents to comply, especially if they car pool or have to unexpectedly arrange for alternate transportation.
"Parents are going to have to measure their kids, carry measuring tape around with them, carry birth certificates around with them," said Rep. Charlie Howard, a Sugar Land Republican. "I think this is ill-advised and is going to cause an undue burden."
Vaught called the argument a "red herring."
When faced with the possibility of a child becoming a paraplegic, "I don't think it's asking too much to have parents plan ahead to accommodate this requirement," Vaught said.
House changes to the bill, approved by a 99-49 vote, still must get final approval in the Senate before it can be sent to the governor.
About 40 other states already require parents to follow the age and height requirements in the bill.
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