To derive the equation of the line through the origin based on the proportional relationship between inches and feet, we need to understand the relationship given the point (3, 36) on the graph.
Here, \( x \) represents the number of feet, and \( y \) represents the number of inches.
First, let's interpret the coordinates:
- \( x = 3 \) feet
- \( y = 36 \) inches
We know that there are 12 inches in a foot. Thus, we can express the inches in terms of feet with the formula:
\[ y = 12x \]
To verify this, if \( x = 3 \): \[ y = 12 \times 3 = 36 \]
This matches the point (3, 36).
Since the relationship is linear and passes through the origin (0,0), the equation of the line is indeed:
\[ y = 12x \]
Therefore, the correct answer is:
B. y = 12x
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