Pick one point from a table, plug its $x$ and $y$ into the inequality, and see if the left side is less than or equal to the right side. Is the resulting statement true or false?

Because each table must contain only points that satisfy the inequality, if you find even one point in a table that makes the inequality false, you can cross out that entire answer choice.

The inequality is $\le$, not just $<$. If a point makes the two sides equal, it still satisfies the inequality.

In Desmos, type y <= -1/2 x + 4. You should see a line with a shaded region below (and including) the line.

For one answer choice, enter its three points as separate expressions, like (x1, y1), (x2, y2), (x3, y3) using the coordinates from that table. Desmos will show them as dots on the graph.

Look to see if all three points from that table lie in the shaded region or exactly on the boundary line. If any point is above the shaded area (outside the solution region), that table cannot be correct. Repeat this for the other tables and identify which table’s three points are all inside or on the shaded region.

A point $(x,y)$ satisfies the inequality $y \le -\tfrac{1}{2}x + 4$ if, when you plug that $x$ and $y$ into the inequality, the statement you get is true.

So for any point:

• Replace $x$ with the $x$-value from the table.
• Replace $y$ with the $y$-value from the table.
• Check whether the left side is less than or equal to the right side.

Take a sample point, say $(2,3)$ (just to learn the process).

Substitute $x=2$ and $y=3$ into the inequality:

Compute the right side:

So we are checking $3 \le 3$, which is true. This is how you will check each point from the tables.

Because the question says the table must contain only $(x,y)$ pairs that satisfy the inequality, if even one pair in a table makes the inequality false, that entire table is wrong.

Check each incorrect choice quickly using one point:

• Choice B, first row $(0,5)$:

This is $5 \le 4$, which is false. So table B is out.

• Choice C, first row $(-4,7)$:

This is $7 \le 6$, which is false. So table C is out.

• Choice D, first row $(0,4)$:

This is $4 \le 4$, which is true, so we must also check another row.

Second row of D is $(2,4)$:

This is $4 \le 3$, which is false, so table D is also out.

Now check each point in the remaining table (choice A):

1. $(-2,3)$:

So $3 \le 5$ is true.

2. $(4,1)$:

So $1 \le 2$ is true.

3. $(6,0)$:

So $0 \le 1$ is true.

All three points in this table satisfy the inequality, and we already saw every other table has at least one point that does not. Therefore, the correct answer is choice A.