Question

What is the constant of proportionality for the relationship shown in this table?

x 2 4 6 8
y 1 2 3 4
Responses

12
1 over 2

2
2

4
4

8

Answer 1

To find the constant of proportionality in the relationship shown in the table, we can compute the ratio \( \frac{y}{x} \) for any pair of values of \( x \) and \( y \).

Let's look at the pairs provided:

1. For \( x = 2 \): \( y = 1 \) → \( \frac{y}{x} = \frac{1}{2} \)
2. For \( x = 4 \): \( y = 2 \) → \( \frac{y}{x} = \frac{2}{4} = \frac{1}{2} \)
3. For \( x = 6 \): \( y = 3 \) → \( \frac{y}{x} = \frac{3}{6} = \frac{1}{2} \)
4. For \( x = 8 \): \( y = 4 \) → \( \frac{y}{x} = \frac{4}{8} = \frac{1}{2} \)

In each case, the ratio \( \frac{y}{x} \) is consistently \( \frac{1}{2} \).

Thus, the constant of proportionality for the relationship shown in this table is \( \frac{1}{2} \).