Next week, the Arlington City Council will consider banning the use of handheld cell phones in cars.
If the measure passes, drivers in Arlington would face a fine for texting or talking on the phone without using a hands-free device.
El Paso, Austin and San Antonio all have similar ordinances.
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According to Arlington's website, its plan models El Paso's, the strictest in the state.
The proposal comes just one month after Gov. Rick Perry vetoed a no-texting-and-driving bill.
Driver Brenda Weaver said she supports the proposed ordinance, saying cellphone use causes accidents.
"There's never a time where you don't see someone swerving because they're on the phone," she said.
She said a friend's child died when they were T-boned by a driver who was on a cellphone.
At Tuesday's meeting, the City Council will hear the plan in its entirety and then decide what parts work and what parts don't.
It could be weeks, if not months, before a version of the plan passes. City officials said there is also a chance that council members will not be able to come to an agreement.