Question

Janice has a pasta recipe that calls for 2 ounces of cheese for every 3 ounces of cooked pasta. Which graph shows this relationship between cheese and pasta?
A.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (2, 3), (4, 6) and (6, 9).

B.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (3, 2), (6, 4), and (9, 6).

C.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (2, 2), (4, 4), (6, 6), (8, 8) and (10, 10).

D.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (5, 2) and (10, 4).

Answer 1

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).