Doesthepoint(–2, 1)satisfytheinequality
y
 ≤ 
1
2
x
 + 	2
?


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?

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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.

Does the point (–2, 1) satisfy the inequality y ≤ 1/2x + 2?

Determine if the point (-2, 1) satisfies the inequality y ≤ 1/2x + 2 by substituting values into the inequality. This example explains the process of verifying inequalities using substitution and is ideal for Grades 7-8 students learning about coordinate geometry and linear inequalities.

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