To find the missing value in the table and assume a linear relationship between \( x \) and \( y \), we first need to establish a linear equation of the form:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
From the provided data:
For the values of \( x \):
- \( x = 1 \), \( y = 12 \)
- \( x = 2 \), \( y = 14 \)
- \( x = 3 \), \( y = 16 \)
- \( x = 4 \), \( y = 18 \)
- \( x = 5 \), \( y = ? \)
Let's calculate the slope \( m \) using the first two points:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{14 - 12}{2 - 1} = \frac{2}{1} = 2 \]
Now we can use the slope to find the linear equation. We can use one of the known points to solve for \( b \).
Using the point \( (1, 12) \):
\[ y = mx + b \implies 12 = 2(1) + b \implies 12 = 2 + b \implies b = 12 - 2 = 10 \]
The equation of the line is:
\[ y = 2x + 10 \]
Now we can substitute \( x = 5 \) to find the missing value of \( y \):
\[ y = 2(5) + 10 = 10 + 10 = 20 \]
Thus, the missing value when \( x = 5 \) is:
\[ \boxed{20} \]