The legislative branch has the job of legislating, or writing and approving the laws. This branch is split into the House of Representatives and the Senate. The election process for the members are determined by each state individually. An intriguing fact is that the members of this branch shall not be questioned in any other place than the House or Senate floor for any speech or debate. I have noticed that in recent confirmation hearings people have stated they cannot speak to hypothetical situations that may be before their desk in instances of judges and high level executive positions. I am curious how this pertains to lobbyists though.
The House of Representatives has representation that is the same as direct taxation on the states. This means as population increases in a state, that state has a higher say in the House of Representatives and must also shoulder a larger share of the tax burden. This was written prior to the 16th Amendment, which allows the federal government to levy income tax directly on citizens. It is interesting how this would have encouraged representatives with larger say to decrease taxes as their states would have to pay more. Additionally, all tax bills must originate in the House of Representatives, although the Senate may propose amendments. This is quite interesting as the Senate recently introduced a budget that has passed a Senate vote regarding funding (FY 2025 Budget Resolution). However, this perhaps does not have to do with taxing and "raising Revenue" as Article I Section 7 of the US Constitution stipulates, but rather just how the money is being spent.
Regarding the relationship between the executive and the House, the executive must request the states to conduct elections at any time when there is a vacancy in the house. Additionally, it the House of Representatives job to vote on impeachment. When politicians are impeached it is determined that there is enough of a case against them for the Senate to determine if the politician should not be permitted to maintain their office. Additionally, the House of Representatives has complete autonomy over their Speaker and other officers.
The Senate is the smaller of the 2 houses with 2 representatives from each state who are elected every 6 years. This form of representation was conducted to protect states' rights by ensuring each state has an equal say.
The Senate and the Executive branch have an interesting relationship. The vice president is considered to be the President of the Senate and breaks ties in the Senate. However, the Senate has the exclusive authority to rule on cases of impeachment, which cannot extend further than removal from office. Additionally, a politician first has to be impeached by the House of Representatives. The president can appoint senators when vacancies occur until the state can appoint a new senator.