Final answer:
The statement is false; the governor of Texas does possess the power to use a line-item veto on appropriation bills.
Step-by-step explanation:
The statement that in Texas, the line-item veto does not exist is false. A line-item veto is a special form of veto that allows a governor to nullify specific provisions of a bill, usually budget appropriations, without rejecting the entire legislative act. In Texas, the governor does have the power to use a line-item veto on appropriation bills. This means that while the governor can approve the overall spending plan, they can strike specific expenditures they oppose.
The line-item veto at the federal level had a brief existence when it was granted to the president in 1996 but was declared unconstitutional by the Supreme Court in 1998. The Supreme Court concluded that the law which granted this power did not align with the U.S. Constitution. However, this does not affect state governors, and many states, including Texas, permit the use of the line-item veto for state budgets.