Question

the table below shows how many pizzas (y) kennetth can make per hour (x). determine if the relationship is proportional and if so, it's constant rate of proportionality.
x: 0 1 2 3 4
y: 0 4 8 12 16


14
1 fourth

4
4

8
8

It is not proportional

Answer 1

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):

1. For \( x = 1 \), \( \frac{y}{x} = \frac{4}{1} = 4 \)
2. For \( x = 2 \), \( \frac{y}{x} = \frac{8}{2} = 4 \)
3. For \( x = 3 \), \( \frac{y}{x} = \frac{12}{3} = 4 \)
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**.