To derive the equation of the line through the origin that represents the proportional relationship between inches and feet, we know that there are 12 inches in a foot. Thus, the relationship can be represented by:
\[ \text{feet} = \frac{1}{12} \times \text{inches} \]
To express this in the familiar linear form \( y = mx \) where \( m \) is the slope, we rearrange it:
\[ y = \frac{1}{12}x \]
However, none of the given options appears to match this. So let's assume the variable \( x \) represents feet and \( y \) represents inches. In that case, the relationship would be:
\[ y = 12x \]
This means for every one foot (x), there are 12 inches (y). So, based on the options provided:
- 0y = 36x
- O y=2x
- O y=12x
- Oy= h2
The correct equation representing the relationship would be:
y = 12x
Thus, the correct answer is: O y = 12x.