**Determine which ordered pairs are part of the solution set for each inequality.**

*y**x*1,{(1,0),(3,2),(2,5),(2,1)}

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

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

1. **For \( (1, 0) \):**
   \[
   y = 0 \quad \text{and} \quad x + 1 = 1 + 1 = 2
   \]
   \( y \leq x + 1 \) becomes \( 0 \leq 2 \), which is true.

2. **For \( (3, 2) \):**
   \[
   y = 2 \quad \text{and} \quad x + 1 = 3 + 1 = 4
   \]
   \( y \leq x + 1 \) becomes \( 2 \leq 4 \), which is true.

3. **For \( (2, 5) \):**
   \[
   y = 5 \quad \text{and} \quad x + 1 = 2 + 1 = 3
   \]
   \( y \leq x + 1 \) becomes \( 5 \leq 3 \), which is false.

4. **For \( (-2, 1) \):**
   \[
   y = 1 \quad \text{and} \quad x + 1 = -2 + 1 = -1
   \]
   \( y \leq x + 1 \) becomes \( 1 \leq -1 \), which is false.

### Solution:
The ordered pairs that satisfy the inequality \( y \leq x + 1 \) are:
\[
\{(1, 0), (3, 2)\}
\]

Would you like more details or have any questions?

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1. How do we graph the inequality \( y \leq x + 1 \)?
2. What does it mean geometrically when a point satisfies an inequality?
3. How can we determine the boundary line for \( y \leq x + 1 \)?
4. What are the steps to solve linear inequalities involving two variables?
5. How does the inequality change if we consider \( y < x + 1 \)?

**Tip:** Always plot the boundary line first when dealing with inequalities to understand which side of the line the solution set lies on.

Explore how to determine which ordered pairs satisfy the inequality y ≤ x + 1 through detailed examples and explanations. This problem involves coordinate geometry and inequalities, suitable for Grades 7-9.

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