Question

find the constant of proportionality.
x | y
2 | 8
3 | 12
4 | 16

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using the first pair of values

Using \( x = 2 \) and \( y = 8 \), we substitute into the formula: \( k=\frac{8}{2}=4 \).

Step3: Verify with other pairs (optional but good practice)

Using \( x = 3 \) and \( y = 12 \): \( k=\frac{12}{3}=4 \). Using \( x = 4 \) and \( y = 16 \): \( k=\frac{16}{4}=4 \). All pairs give the same \( k \).

Answer:

The constant of proportionality is \( 4 \).