To find the correct graph that represents the relationship between cheese and cooked pasta based on the given ratio (2 ounces of cheese for every 3 ounces of cooked pasta), we should analyze the ratio.
The relationship can be expressed as:
\[ \text{cheese} = \frac{2}{3} \times \text{pasta} \]
This means that for every 3 ounces of pasta, you need 2 ounces of cheese. We can calculate some points using this ratio:
- If pasta = 0 ounces, cheese = \( \frac{2}{3} \times 0 = 0 \) ounces.
- If pasta = 3 ounces, cheese = \( \frac{2}{3} \times 3 = 2 \) ounces.
- If pasta = 6 ounces, cheese = \( \frac{2}{3} \times 6 = 4 \) ounces.
- If pasta = 9 ounces, cheese = \( \frac{2}{3} \times 9 = 6 \) ounces.
Now, let's evaluate the given graph options:
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Option A: The line passes through (2, 3), (4, 6), and (6, 9). This suggests a ratio of 3 ounces of pasta for every 2 ounces of cheese; this is incorrect.
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Option B: The line passes through (3, 2), (6, 4), and (9, 6). This follows the correct ratio of 2 ounces of cheese for every 3 ounces of pasta. This option is correct.
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Option C: The line passes through points that suggest a 1:1 ratio which does not match the given ratio; this is incorrect.
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Option D: The pairs (5, 2) and (10, 4) suggest a different ratio that does not match the specified needs; this is incorrect.
The right choice is B, which correctly represents the relationship between cheese and pasta using the specified ratio of 2 ounces of cheese for every 3 ounces of cooked pasta.