To identify the graph that represents the inequality $x \geq 2$, let's analyze each option.

1. Inequality: $x \geq 2$ implies that the shaded region should include all points where $x$ is greater than or equal to $2$.
2. Line: The boundary line should be at $x = 2$. Since it is $\geq$ (greater than or equal to), the line itself should be solid, indicating that points on the line $x = 2$ are included in the solution.
3. Shaded Region: The shading should be on the right side of this line, where $x$ values are greater than 2.

Analysis of Each Graph:

• Top left: Shows a solid vertical line at $x = 2$ with shading to the right, representing $x \geq 2$. This graph is correct.
• Top right: Shaded to the left of the line $x = 2$, which represents $x \leq 2$.
• Bottom left: Shaded to the right of the line $x = 2$, but the line is dashed, indicating $x > 2$ (not $x \geq 2$).
• Bottom right: Shaded to the left of a dashed line at $x = 2$, which represents $x < 2$.

Conclusion:

The correct answer is the top left graph, as it correctly represents $x \geq 2$ with a solid line at $x = 2$ and shading to the right.

Would you like more details on solving inequalities or graph interpretation?

Related Questions:

1. How do you graph inequalities on a coordinate plane?
2. What is the difference between a solid line and a dashed line in inequality graphs?
3. How do you determine the direction of shading in inequality graphs?
4. What are the steps to solve a linear inequality and graph it?
5. How can inequalities be used to define regions in real-world applications?

Tip: For inequalities with "greater than or equal to" or "less than or equal to," use a solid line; for strict inequalities, use a dashed line.