Pick one answer choice and test its first point: compute $-3x+7$ for that x-value and see whether the inequality $y \le$ (that result) is true. If it fails for even one point, that entire answer choice cannot be correct.

Because the inequality is $y \le -3x+7$, points where $y$ is exactly equal to $-3x+7$ do count as solutions. Do not discard points just because $y$ equals $-3x+7$ instead of being smaller.

You do not need to check every point in a table if you already find one that does not satisfy the inequality—cross off that choice and move on to the next.

In Desmos, type y <= -3x + 7. You should see the line $y=-3x+7$ with shading on one side—this shaded region (including the line itself) represents all solutions to the inequality.

For a chosen table, enter each point as its own expression, such as (2,2), (1,5), (0,8) for option A. Desmos will display these as dots on the graph.

Look to see if each dot lies either exactly on the line $y=-3x+7$ or inside the shaded region. If any point is outside the shaded area (above the line), that answer choice is not correct. Repeat this process with the other tables until you find a table where all its points lie in the shaded region or on the boundary line; that table’s pairs are all solutions to the inequality.

An ordered pair $(x,y)$ is a solution to the inequality $y \le -3x+7$ if, when you plug the x-value into $-3x+7$, the resulting value is greater than or equal to the given y-value.

In other words, for each point, compute $-3x+7$ and check whether $y \le -3x+7$.

Option A has points $(2,2)$, $(1,5)$, and $(0,8)$.

• For $(2,2)$:
  $-3(2)+7 = -6+7 = 1$.
  Check: Is $2 \le 1$? No. So $(2,2)$ is not a solution.

Since even one point in the table is not a solution, the entire table for option A cannot be correct.

Option B has $(2,4)$, $(-1,7)$, and $(3,-3)$.

• For $(2,4)$:
  $-3(2)+7 = 1$.
  Check: Is $4 \le 1$? No. So option B is eliminated.

Option D has $(2,3)$, $(-1,10)$, and $(4,-6)$.

• For $(2,3)$:
  $-3(2)+7 = 1$.
  Check: Is $3 \le 1$? No. So option D is also eliminated.

So far, none of these tables have all their points satisfying the inequality.

Option C has $(2,1)$, $(0,7)$, and $(3,-2)$.

• For $(2,1)$:
  $-3(2)+7 = -6+7 = 1$.
  Check: Is $1 \le 1$? Yes.
• For $(0,7)$:
  $-3(0)+7 = 0+7 = 7$.
  Check: Is $7 \le 7$? Yes.
• For $(3,-2)$:
  $-3(3)+7 = -9+7 = -2$.
  Check: Is $-2 \le -2$? Yes.

All three ordered pairs in this table satisfy $y \le -3x+7$, so choice C is the correct answer.