Determine the values of a, b, c, m, and n using the given rules and tables.

Given $y=4$ and the rule $y = x - 9$.

$$4 = a - 9$$

Add 9 to both sides:

$$a = 4 + 9$$ $$a = 13$$

Given $x=20$ and the rule $y = x - 9$.

$$b = 20 - 9$$ $$b = 11$$

Given $x=100$ and the rule $y = x - 9$.

$$c = 100 - 9$$ $$c = 91$$

The values are: $\boxed{a = 13, b = 11, c = 91}$

From the table, when $x=8$, $y=m$. Using the given rule $y = x + 7$:

$$m = 8 + 7$$ $$m = 15$$

From the table, when $x=9$, $y=n$. Using the given rule $y = x + 7$:

$$n = 9 + 7$$ $$n = 16$$

The values are: $\boxed{m = 15, n = 16}$