To determine if the point $(-2, 1)$ satisfies the inequality $y \leq \frac{1}{2}x + 2$, we can substitute $x = -2$ and $y = 1$ into the inequality:

1. Substitute $x = -2$ into the right side of the inequality:

   $\frac{1}{2}(-2) + 2 = -1 + 2 = 1$

2. Now we have the inequality:

   $y \leq 1$

3. Substitute $y = 1$ from the point into this inequality:

   $1 \leq 1$

Since $1 \leq 1$ is true, the point $(-2, 1)$ does satisfy the inequality $y \leq \frac{1}{2}x + 2$.

Would you like more details or have any questions?

---

1. What if the inequality was $y < \frac{1}{2}x + 2$? Would the point still satisfy it?
2. How would you graph this inequality on the coordinate plane?
3. Can you verify if the inequality is satisfied for other points like $(0, 2)$?
4. How does changing the slope in the inequality affect the solution set?
5. How would you solve if the inequality had a strict inequality symbol?

Tip: Always substitute values directly into inequalities and simplify carefully to verify if they satisfy the condition.