if one were  to graph the solution to the following inequality:
y > 2x + 3
which of the following coordinates would be in the region indicated by in the inequality equation above?

a. (2,2)
b. (2, -2)
c. (-2,2)
d. (-2,-2)
e. (2,3)

To solve this problem, we need to determine which of the given points lies in the region where the inequality \( y > 2x + 3 \) is true.

### Step 1: Understand the Inequality
The inequality \( y > 2x + 3 \) describes a region above the line \( y = 2x + 3 \) on a graph.

### Step 2: Substitute the Coordinates into the Inequality
We will substitute each point into the inequality to see if it satisfies the condition \( y > 2x + 3 \).

1. **Point (2,2):**
   \[
   y = 2 \quad \text{and} \quad 2x + 3 = 2(2) + 3 = 4 + 3 = 7
   \]
   \( 2 > 7 \) is false.

2. **Point (2,-2):**
   \[
   y = -2 \quad \text{and} \quad 2x + 3 = 2(2) + 3 = 4 + 3 = 7
   \]
   \( -2 > 7 \) is false.

3. **Point (-2,2):**
   \[
   y = 2 \quad \text{and} \quad 2x + 3 = 2(-2) + 3 = -4 + 3 = -1
   \]
   \( 2 > -1 \) is true.

4. **Point (-2,-2):**
   \[
   y = -2 \quad \text{and} \quad 2x + 3 = 2(-2) + 3 = -4 + 3 = -1
   \]
   \( -2 > -1 \) is false.

5. **Point (2,3):**
   \[
   y = 3 \quad \text{and} \quad 2x + 3 = 2(2) + 3 = 4 + 3 = 7
   \]
   \( 3 > 7 \) is false.

### Conclusion:
The only point that satisfies the inequality \( y > 2x + 3 \) is **(c) (-2,2)**.

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Would you like more details or have any questions? Here are some related questions to consider:

1. What is the slope-intercept form of a linear equation?
2. How do you graph a linear inequality on a coordinate plane?
3. What changes if the inequality is \( y \geq 2x + 3 \) instead of \( y > 2x + 3 \)?
4. How do you find the x- and y-intercepts of the line \( y = 2x + 3 \)?
5. What does the inequality \( y < 2x + 3 \) represent on the graph?

**Tip:** When graphing an inequality, remember that if the inequality is strict (i.e., \( > \) or \( < \)), the boundary line is dashed. If it is non-strict (i.e., \( \geq \) or \( \leq \)), the boundary line is solid.

Explore how to graph the inequality y > 2x + 3 and determine which coordinates lie in the indicated region. This problem involves analyzing linear inequalities in coordinate geometry and understanding their graphical representation. Suitable for Grades 9-12.

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