Question

The table below shows how many pizzas (y) Kenneth 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 0
y 4 8 12 16

14
1 fourth

4
4

8
8

It is not proportional

Answer 1

To determine if the relationship between x (the number of hours) and y (the number of pizzas) is proportional, we can check two things:

1. **The origin**: A relationship is proportional if it passes through the origin (0, 0).
2. **Constant ratio**: We calculate the ratio of y to x (y/x) for the given values of x and see if it remains constant.

From the table, the points are:
- (0, 4)
- (1, 8)
- (2, 12)
- (3, 16)
- (4, 20)

Now let's identify the points correctly. The correct point matching your description seems to be:

- x = 0, y = 0 (This is not listed; it should actually be (0, 0) for proportionality)
- x = 1, y = 4 (Not spelled out clearly, but it implies the first case)
- x = 2, y = 8
- x = 3, y = 12
- x = 4, y = 16

Next, we can calculate the ratio of y to x:

- For x = 1, y = 4: Ratio = \( \frac{4}{1} = 4 \)
- For x = 2, y = 8: Ratio = \( \frac{8}{2} = 4 \)
- For x = 3, y = 12: Ratio = \( \frac{12}{3} = 4 \)
- For x = 4, y = 16: Ratio = \( \frac{16}{4} = 4 \)

Since the ratio y/x is constant and equals 4 for all the non-zero values of x, we can conclude that this relationship is indeed proportional.

Therefore, the constant rate of proportionality is **4**.

Hence, the answer is **4**.