1. The problem states the relationship between the number of ravioli $r$ and the number of people $y$ as $y = \frac{1}{4}r$. 2. This means for every 4 ravioli, there is 1 person. The formula used is a direct proportionality: $$y = \frac{1}{4}r$$ where $y$ is the number of people and $r$ is the number of ravioli. 3. To find the number of people when $r = 48$, substitute $48$ into the formula: $$y = \frac{1}{4} \times 48$$ 4. Simplify the multiplication: $$y = \frac{1}{4} \times 48 = \frac{48}{4}$$ 5. Simplify the fraction by canceling common factors: $$y = \frac{\cancel{48}}{\cancel{4}} = 12$$ 6. Therefore, when there are 48 ravioli, the number of people is $12$. Final answer: $$y = 12$$