Context: A table works only if every $(x, y)$ pair satisfies both $y < -6x - 22$ and $y > -4x - 7$, i.e. each $y$ lies strictly between $-4x - 7$ and $-6x - 22$.

Answer: D) the table with pairs $(-9, 30)$, $(-10, 37)$, $(-12, 48)$

Why: At $x = -9$ the bounds are $-4(-9) - 7 = 29$ and $-6(-9) - 22 = 32$, and $29 < 30 < 32$. At $x = -10$ they are $33$ and $38$, and $33 < 37 < 38$. At $x = -12$ they are $41$ and $50$, and $41 < 48 < 50$. All three rows satisfy both inequalities.

Traps:

• A) Fails at $(-9, 27)$: $27 > -4(-9) - 7 = 29$ is false; the row $(-10, 51)$ also breaks $y < -6x - 22$ since $51 < 38$ is false.
• B) $(-9, 32)$ lands exactly on the boundary value $-6(-9) - 22 = 32$, and the inequality $y < -6x - 22$ is strict.
• C) $(-9, 28)$ fails $y > -4x - 7$ because $28 > 29$ is false.