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:
- For \( p = 2 \): \[ c = \frac{2}{3} \cdot 2 = \frac{4}{3} \quad (\text{but it shows } 3) \]
- For \( p = 4 \): \[ c = \frac{2}{3} \cdot 4 = \frac{8}{3} \quad (\text{but it shows } 6) \]
- 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:
- For \( p = 3 \): \[ c = \frac{2}{3} \cdot 3 = 2 \quad (\text{correct, shows } 2) \]
- For \( p = 6 \): \[ c = \frac{2}{3} \cdot 6 = 4 \quad (\text{correct, shows } 4) \]
- 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:
- For \( p = 5 \): \[ c = \frac{2}{3} \cdot 5 = \frac{10}{3} \quad (\text{not } 2) \]
- 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
1 answer