Question

assuming a linear relationship, find the missing value in the table below. x 1 2 3 4 5 y 6 10 14 18

Explanation:

Step1: Find the common difference

To find the common difference between consecutive \( y \)-values, we subtract the previous \( y \)-value from the next one. For example, \( 10 - 6 = 4 \), \( 14 - 10 = 4 \), \( 18 - 14 = 4 \). So the common difference \( d = 4 \).

Step2: Calculate the missing \( y \)-value

The last given \( y \)-value is \( 18 \) when \( x = 4 \). For \( x = 5 \), we add the common difference to \( 18 \). So \( 18 + 4 = 22 \).

Answer:

\( 22 \)