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:

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.