Final answer:
The rejection of a bill by the governor is known as a veto, which is a formal power allowing them to refuse to sign a bill into law.
Step-by-step explanation:
When the governor in the state rejects a bill that has been passed by the state's legislature, this action is known as a veto.
The veto is one of the formal powers that governors have, allowing them to refuse to sign a bill into law. Depending on the specifics of state law, governors may also have other veto powers such as the line-item veto and the amendatory veto. An amendatory veto allows a governor to send a bill back to the legislature with a message requesting a specific amendment. Conversely, a line-item veto lets the governor strike out specific parts of a bill, such as budget lines, while approving the rest.