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
y 0,4,8,12,16

1/4

4

8

It is not proportional

Answer 1

To determine if the relationship between the number of pizzas (y) that Kenneth can make and the hours (x) he works is proportional, we need to check if the ratio \( \frac{y}{x} \) remains constant for all values of \( x \) and \( y \).

Let's calculate the ratios for the given values:

- For \( x = 1 \), \( y = 4 \):
\( \frac{y}{x} = \frac{4}{1} = 4 \)

- For \( x = 2 \), \( y = 8 \):
\( \frac{y}{x} = \frac{8}{2} = 4 \)

- For \( x = 3 \), \( y = 12 \):
\( \frac{y}{x} = \frac{12}{3} = 4 \)

- For \( x = 4 \), \( y = 16 \):
\( \frac{y}{x} = \frac{16}{4} = 4 \)

Since the ratio \( \frac{y}{x} \) is constant (equal to 4) for all pairs of values, we can conclude that the relationship is proportional.

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