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 representing the relationship between cheese and pasta according to Janice's recipe, we need to establish the ratio provided.

The recipe calls for **2 ounces of cheese for every 3 ounces of cooked pasta**. This can be expressed as a fraction:

\[
\frac{\text{cheese}}{\text{pasta}} = \frac{2}{3}
\]

From this ratio, we can determine how much cheese corresponds to any amount of pasta. If we let \( p \) represent the amount of pasta (in ounces) and \( c \) represent the amount of cheese (in ounces), we can write the relationship as:

\[
c = \frac{2}{3}p
\]

Now we can check each of the provided graphs to see which one fits this equation.

**Graph A** passes through:
- (0, 0)
- (2, 3)
- (4, 6)
- (6, 9)

Checking the points:
1. For \( p = 2 \):
\[
c = \frac{2}{3} \cdot 2 = \frac{4}{3} \quad (\text{but it shows } 3)
\]
2. For \( p = 4 \):
\[
c = \frac{2}{3} \cdot 4 = \frac{8}{3} \quad (\text{but it shows } 6)
\]
3. For \( p = 6 \):
\[
c = \frac{2}{3} \cdot 6 = 4 \quad (\text{but it shows } 9)
\]

**Graph B** passes through:
- (0, 0)
- (3, 2)
- (6, 4)
- (9, 6)

Checking the points:
1. For \( p = 3 \):
\[
c = \frac{2}{3} \cdot 3 = 2 \quad (\text{correct, shows } 2)
\]
2. For \( p = 6 \):
\[
c = \frac{2}{3} \cdot 6 = 4 \quad (\text{correct, shows } 4)
\]
3. For \( p = 9 \):
\[
c = \frac{2}{3} \cdot 9 = 6 \quad (\text{correct, shows } 6)
\]

**Graph C**: This graph passes through
- (0, 0)
- (2, 2)
- (4, 4)
- (6, 6)
- (8, 8)
- (10, 10)

However, it shows a 1 to 1 ratio, which does not match our recipe.

**Graph D**:
- (0, 0)
- (5, 2)
- (10, 4)

Checking the points:
1. For \( p = 5 \):
\[
c = \frac{2}{3} \cdot 5 = \frac{10}{3} \quad (\text{not } 2)
\]
2. Similarly, for \( p = 10 \):
\[
c = \frac{2}{3} \cdot 10 = \frac{20}{3} \quad (\text{not } 4)
\]

Thus, the only graph that accurately represents the relationship of \( c = \frac{2}{3}p \) is **Graph B**.

So the correct answer is:

**B**