To find the correct graph that represents the relationship between cheese and pasta according to Janice's recipe, we first need to understand the ratio given in the recipe: 2 ounces of cheese for every 3 ounces of cooked pasta.
This can be expressed as a ratio:
\[ \text{Cheese} : \text{Pasta} = 2 : 3 \]
We can convert this ratio into an equation. If we let \( C \) be the amount of cheese in ounces and \( P \) be the amount of pasta in ounces, the relationship can be expressed as:
\[ \frac{C}{P} = \frac{2}{3} \]
From this, we can derive the amount of cheese based on pasta:
\[ C = \frac{2}{3} P \]
Now, we can identify specific points based on this equation. For instance:
- When \( P = 0 \), \( C = 0 \)
- When \( P = 3 \), \( C = 2 \) (point (3, 2))
- When \( P = 6 \), \( C = 4 \) (point (6, 4))
- When \( P = 9 \), \( C = 6 \) (point (9, 6))
- When \( P = 0 \), \( C = 0 \)
- When \( P = 12 \), \( C = 8 \) (not among the options)
Now, let's analyze the provided options:
- A. (0, 0), (2, 3), (4, 6), (6, 9) — This shows a relationship of cheese to pasta that does not match \( C = \frac{2}{3} P \) (incorrect).
- B. (0, 0), (3, 2), (6, 4), (9, 6) — This correctly has the points derived from the ratio \( C = \frac{2}{3} P \) (correct).
- C. (0, 0), (2, 2), (4, 4), (6, 6), (8, 8), (10, 10) — This shows equal amounts of cheese and pasta (incorrect).
- D. (0, 0), (5, 2), (10, 4) — This configuration does not fit the ratio \( C = \frac{2}{3} P \) (incorrect).
Based on this analysis, the correct answer is:
B. The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y-axis showing an upward-facing line starting (0, 0) and passing through the points (3, 2), (6, 4), and (9, 6).
1 answer