Why do an eye and pyramid appear on the one dollar bill?

Interesting question! Over the years, many conspiracy theorists have hypothesized that the eye and pyramid represent the preeminent symbols of the Illuminati. The Illuminati is said to be a secret organization of global elites who are working to enslave the whole world. Conspiracy theorists believe that the All-Seeing Eye represents the eye of Horus or Lucifer.
The uncapped pyramid is said to represent an unfinished order of business: the Old World Order has yet to be destroyed; thus, it stands in the way of the New World Order ("Novus Ordo Seclorum" on the one dollar bill). Conspiracy theorists also believe that the thirteen steps of the pyramid represent the thirteen bloodlines of the Illuminati that have pledged allegiance to Lucifer. Despite these claims, other experts believe that the truth is a little less exciting.
It was Franklin Delano Roosevelt (the 32nd President of the United States) who commissioned the eye and pyramid to be included on the dollar bill in 1935. The original eye and pyramid was first included in the back of the United States Great Seal in 1782. The thirteen steps of the pyramid signified that America was yet an unfinished nation. Perhaps the thirteen steps represented the first thirteen colonies of the United States.
For Franklin Roosevelt (who was a Mason), the eye represented the all-seeing eye of Providence or what Masons call The Great Architect. The accompanying words "Annuit Coeptis" translates as "God has favored our undertakings." On the pyramid, the Roman numerals MDCCLXXVI represent the advent of the United States in 1776. (M=1000 D= 500 C=100 L=50 X=10 VI=6). Roosevelt was impressed with the idea of the all-seeing eye of God presiding over the affairs of the United States, so he commissioned the eye and pyramid to be included on the one dollar bill.
While conspiracy theorists claim that, as a Mason, Franklin Roosevelt was part of the Illuminati effort to enslave the whole world, the truth is that the president just appreciated what the symbols represented. He simply liked the idea of an all-seeing Providence presiding over the affairs of an unfinished nation.
For more, please refer to the authoritative links below. For those who are curious about the conspiracy theory behind the eye and pyramid symbol, the following informational link may prove helpful: The Illuminati Symbol, the Great Seal, and the One Dollar Bill.
 
 
http://greatseal.com/dollar/hawfdr.html

http://web.mit.edu/afs/athena.mit.edu/user/d/r/dryfoo/www/Masonry/Essays/eyepyr.html

https://money.howstuffworks.com/symbols-dollar-bill.htm