To represent the equation $9x - 6y = 16$ in a table, we can solve for $y$ in terms of $x$ or vice versa. Let's solve for $y$:

$9x - 6y = 16$

Rearrange the equation to isolate $y$:

$-6y = 16 - 9x$

Now divide by -6:

$y = \frac{9x - 16}{6}$

Now we can generate a table of values for $x$ and $y$ by substituting different values of $x$ into the equation.

Here is a sample table for values of $x$ from -2 to 2:

$x$	$y$
-2	$\frac{9(-2) - 16}{6} = \frac{-18 - 16}{6} = \frac{-34}{6} = -\frac{17}{3}$
-1	$\frac{9(-1) - 16}{6} = \frac{-9 - 16}{6} = \frac{-25}{6}$
0	$\frac{9(0) - 16}{6} = \frac{-16}{6} = -\frac{8}{3}$
1	$\frac{9(1) - 16}{6} = \frac{9 - 16}{6} = \frac{-7}{6}$
2	$\frac{9(2) - 16}{6} = \frac{18 - 16}{6} = \frac{2}{6} = \frac{1}{3}$

This table gives you pairs of $(x, y)$ values that satisfy the equation $9x - 6y = 16$.

Would you like me to calculate more values, or do you have any questions on this approach?

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Related Questions:

1. What happens if you solve the equation for $x$ instead of $y$?
2. How would the table change if the equation were $9x + 6y = 16$?
3. What is the slope of the line represented by the equation $9x - 6y = 16$?
4. How can you graph this equation using the values in the table?
5. How can you check the validity of a solution using substitution?

Tip: When creating a table for linear equations, you can pick values for either variable (x or y) and solve for the other. This makes it easy to visualize the relationship between the two variables.