What does "home rule" mean in Texas?

"Home rule" in Texas refers specifically to the authority of a city to govern itself under its own charter, which is a fundamental aspect of local governance in the state. This concept allows cities with populations of over 5,000 to adopt their own charters, granting them the power to legislate and make decisions that reflect the needs and desires of their local constituents.

This authority includes a wide range of local governance issues, from establishing the structure and responsibilities of the city government to enacting ordinances and regulations tailored to the community. This autonomy distinguishes home rule cities from general law cities, which operate under the state’s general laws with less local discretion.

The other options do not align with the definition of home rule. The authority of the state to govern itself refers to state sovereignty, while the state's ability to establish its own amendments pertains to higher levels of governance. The power of local governments to regulate zoning laws is indeed a function of home rule, but it does not encapsulate the broader concept of what home rule means in Texas.