Final answer:
The suffragists were using their First Amendment rights to freedom of speech and peaceful assembly to advocate for women's suffrage during their White House picketing in 1917.
Step-by-step explanation:
The suffragists picketing at the White House on January 25, 1917, were exercising their First Amendment rights, specifically the rights to freedom of speech and peaceful assembly. By holding signs, wearing banners, and publicly demonstrating, they sought to send their message to President Woodrow Wilson and advocate for an amendment granting women the right to vote. This form of protest was an essential component of their broader efforts, which included legal action, hunger strikes, and civil disobedience, to secure the passage of the Nineteenth Amendment.