To derive the equation of the line that represents the proportional relationship between inches and feet, we need to understand that there are 12 inches in a foot.
This means that for every 12 inches (x), there is 1 foot (y).
To express this relationship as an equation, we can set up the following proportional relationship:
\[ y = \frac{1}{12} x \]
This means for every x inches, y feet is one-twelfth of x.
None of the other options (y = 12x, y = 36x, or y = 2x) accurately represent the conversion from inches to feet.
Thus, the correct equation of the line through the origin is:
\[ y = \frac{1}{12} x \]