To derive the equation of the line that represents the proportional relationship between inches (y) and feet (x) through the origin, we need to use the basic form of a linear equation through the origin, which is \( y = kx \), where \( k \) is the constant of proportionality.
Since there are no specific numbers provided from the graph in your question, let's assume that there is a known conversion factor between inches and feet.
There are 12 inches in a foot, so the conversion factor between inches (y) and feet (x) would be:
\[ y = 12x \]
Therefore, if the relationship is indeed between inches and feet, the correct equation would be:
\( y = 12x \)
If more information or specific points from the graph were provided, it would help confirm the exact values. As is, the correct derived equation representing the relationship is:
y = 12x.