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 determine which graph correctly represents the relationship between cheese and pasta in Janice's recipe, we need to analyze the ratio provided. The recipe states that for every 3 ounces of cooked pasta, 2 ounces of cheese is required.

This means the relationship can be defined as:

- Cheese = (2/3) * Pasta

When plotting this relationship on a graph where "pasta" is along the x-axis and "cheese" is along the y-axis, we can calculate the corresponding amount of cheese for specific amounts of pasta:

- For 0 ounces of pasta, cheese = 0 ounces
- For 3 ounces of pasta, cheese = 2 ounces
- For 6 ounces of pasta, cheese = 4 ounces
- For 9 ounces of pasta, cheese = 6 ounces
- For 12 ounces of pasta, cheese = 8 ounces (but this is outside the 0 to 10 range)

Now let's analyze each option:

A. This option passes through (2, 3), (4, 6), and (6, 9), which does not fit the provided ratio (as these ratios are incorrect according to the 2:3 ratio).

B. This option shows points (3, 2), (6, 4), and (9, 6), which fits the ratio perfectly:
- 3 oz pasta -> 2 oz cheese
- 6 oz pasta -> 4 oz cheese
- 9 oz pasta -> 6 oz cheese

C. This option has equal amounts of cheese and pasta (e.g., (2, 2), (4, 4)), which is not correct according to the recipe.

D. This option shows (5, 2) and (10, 4), which also does not fit the 2:3 ratio of cheese to pasta.

Based on this analysis, the correct answer is **B**.