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The table asks to fill in the values of \( y \) using the function rule \( y = 3 + 6x \). Let's calculate the values for each \( x \) in the table.

### The function is:
\[
y = 3 + 6x
\]

Now, let's calculate \( y \) for each \( x \):

1. **When \( x = 1 \):**
   \[
   y = 3 + 6(1) = 3 + 6 = 9
   \]
   
2. **When \( x = 2 \):**
   \[
   y = 3 + 6(2) = 3 + 12 = 15
   \]
   
3. **When \( x = 6 \):**
   \[
   y = 3 + 6(6) = 3 + 36 = 39
   \]
   
4. **When \( x = 9 \):**
   \[
   y = 3 + 6(9) = 3 + 54 = 57
   \]

### Completed table:
| \( x \) | \( y \)  |
|--------|--------|
| 1      | 9      |
| 2      | 15     |
| 6      | 39     |
| 9      | 57     |

Would you like a more detailed explanation, or do you have any questions?

### Related Questions:
1. What happens to \( y \) if \( x \) increases by a large number?
2. How would you modify the function if you wanted to subtract a value from \( y \)?
3. What is the slope of the function \( y = 3 + 6x \), and how does it affect the graph?
4. Can you graph the function for values of \( x \) from 0 to 10?
5. How would you write a function that decreases \( y \) as \( x \) increases?

### Tip:
The coefficient of \( x \) in a linear function, like the 6 in \( y = 3 + 6x \), determines how fast the value of \( y \) changes as \( x \) increases.

Fill in the table using the function rule y = 3 + 6x.

Fill in the values of y in a table by using the linear function y = 3 + 6x. This exercise demonstrates how to calculate y by substituting x values in the equation. Suitable for students in Grades 6-8.

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