Answer:
Jimmy Carter uses "We are all Americans together, and we must not forget that the common good is our common interest and our individual responsibility" to make an appeal to emotions
Explanation:
Jimmy Carter uses a logical appeal in the first part of the passage when he uses a logic that since that old republic has now spanned over a continent so, has more responsibilities to the secure and prosperous future of the world.
In second part he uses an appeal to fear by mentioning single-issue groups and special organizations and calling it a disturbing factor which distort nation's purpose.
In the last part he uses an appeal to emotions by calling Americans a united nation, by calling everyone American. It invokes emotion of patriotism in the audience. Hence this lines best uses an emotional appeal.