To determine which ordered pairs are part of the solution set for the inequality $y \geq 2x$, we will check each ordered pair given in the set $\{(2, 6), (0, -1), (3, 5), (-1, -2)\}$.

Let's evaluate each pair $(x, y)$:

1. For $(2, 6)$: $y = 6 \quad \text{and} \quad 2x = 2(2) = 4$ $y \geq 2x$ becomes $6 \geq 4$, which is true.

2. For $(0, -1)$: $y = -1 \quad \text{and} \quad 2x = 2(0) = 0$ $y \geq 2x$ becomes $-1 \geq 0$, which is false.

3. For $(3, 5)$: $y = 5 \quad \text{and} \quad 2x = 2(3) = 6$ $y \geq 2x$ becomes $5 \geq 6$, which is false.

4. For $(-1, -2)$: $y = -2 \quad \text{and} \quad 2x = 2(-1) = -2$ $y \geq 2x$ becomes $-2 \geq -2$, which is true.

Solution:

The ordered pairs that satisfy the inequality $y \geq 2x$ are: $\{(2, 6), (-1, -2)\}$

Would you like more details or have any questions?

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1. How do you graph the inequality $y \geq 2x$?
2. What is the significance of the equality condition $y = 2x$?
3. How can you test a point to see if it satisfies an inequality?
4. What changes if the inequality is $y > 2x$ instead of $y \geq 2x$?
5. How would the solution set change if the inequality were $y \leq 2x$?

Tip: To verify which side of the boundary line is part of the solution set, pick a test point that is not on the boundary and check if it satisfies the inequality.