Final answer:
The Elkins Act was the Progressive Era law that prohibited rebates for railroad service, complementing the Interstate Commerce Act by ensuring fair competition and pricing.
Step-by-step explanation:
The Progressive Era law that made it illegal to accept or provide rebates for railroad service was the Elkins Act. President Theodore Roosevelt's administration pushed for the passage of this law to curtail the unjust practice of railroads offering rebates and discounts to preferred customers, which was seen as discriminatory and harmful to smaller shippers, particularly farmers.
This law was a complement to the earlier Interstate Commerce Act of 1887, which aimed to regulate the railroad industry and ensure fair pricing for all. With the Elkins Act, the efforts to ensure fair competition were significantly strengthened, making it a pivotal piece of legislation during the Progressive Era.