To solve for the missing value in the table assuming a linear relationship:

1. Observe that as $x$ increases by 1, $y$ increases consistently. This indicates a constant rate of change, or slope.

2. Compute the difference between consecutive $y$-values:

   • $15 - 9 = 6$
   • $21 - 15 = 6$
   • $27 - 21 = 6$

   The slope $m$ is $6$.

3. Using the linear equation $y = mx + b$, where $m = 6$, we solve for the intercept $b$ using a known point, such as $(1, 9)$: $9 = 6(1) + b \implies b = 3$

4. The equation for the relationship is: $y = 6x + 3$

5. Substitute $x = 5$ into the equation: $y = 6(5) + 3 = 30 + 3 = 33$

Missing Value: 33

Would you like more details or further explanation?

Expanding Questions:

1. How would the equation change if the slope were negative?
2. What happens to the table if the relationship is quadratic instead of linear?
3. How do we check the validity of linearity for a given data set?
4. Can you graph this relationship and verify visually?
5. What is the significance of the intercept $b$ in this context?

Tip: Always verify the consistency of a pattern in a table before assuming a specific relationship (e.g., linearity).