To determine if the relationship between the number of pizzas made (y) and the number of hours (x) is proportional, we need to check if there is a constant rate of change between x and y.
From the table you've provided:
- When \( x = 0 \), \( y = 0 \)
- When \( x = 1 \), \( y = 4 \)
- When \( x = 2 \), \( y = 8 \)
- When \( x = 3 \), \( y = 12 \)
- When \( x = 4 \), \( y = 16 \)
To check for proportionality, we can find the ratio \( \frac{y}{x} \) for each pair (except where \( x = 0 \) since division by zero is undefined):
- For \( x = 1 \), \( \frac{y}{x} = \frac{4}{1} = 4 \)
- For \( x = 2 \), \( \frac{y}{x} = \frac{8}{2} = 4 \)
- For \( x = 3 \), \( \frac{y}{x} = \frac{12}{3} = 4 \)
- For \( x = 4 \), \( \frac{y}{x} = \frac{16}{4} = 4 \)
Since the ratio \( \frac{y}{x} \) is consistently equal to 4 for all non-zero values of \( x \), we can conclude that the relationship is indeed proportional.
The constant rate of proportionality is \( 4 \).
So, the answer is that it is proportional and the constant rate of proportionality is 4.