Final answer:
US senators were elected by their state legislatures when Sam Houston served, a practice that continued until the adoption of the Seventeenth Amendment in 1913, which allowed for direct election by the citizens.
Step-by-step explanation:
At the time when Sam Houston served in the US Senate, senators were elected by their state legislatures, not by direct vote of the citizens. This method of election was in practice until the ratification of the Seventeenth Amendment in 1913. As political parties grew and the public became disenchanted with the legislative election system, which was often mired in scandal and perceived cronyism, the push for reform grew.
Consequently, the Seventeenth Amendment made the election process for senators more democratic, allowing them to be elected directly by the people, much like the House of Representatives.