To determine which equation matches the inequality in the given graph, we need to consider the properties of the shading and the line itself.
- The line slopes upward from left to right, indicating that the equation of the line will be in the form \( y = mx + b \), where \( m \) is a positive slope.
- The area that is shaded is to the right of the line, which typically indicates that the inequality will be greater than either \( > \) or \( \geq \).
- The point on the line itself determines whether we include the line in the solution set or not. If the line is included, we use \( \leq \) or \( \geq \); if it is not included, we use \( < \) or \( > \).
Since the shaded area is to the right of the line, we consider the options:
- Option #1: \( y < \frac{3}{2}x + 3 \) means the area below the line is shaded.
- Option #2: \( y \leq \frac{3}{2}x + 3 \) also means the area below or on the line is shaded, which does not match our description.
- Option #3: \( y > \frac{3}{2}x + 3 \) means that the area above the line is shaded, which is not the case here.
- Option #4: \( y \geq \frac{3}{2}x + 3 \) allows for the area on or above the line to be shaded, which does not match the description.
Given that the shaded area is to the right of the line, and if we assume the line has been included, the correct choice is:
Option #4: \( y \geq \frac{3}{2}x + 3 \).
Therefore, the equation that matches the graph is Option 4.
1 answer