The graph shows a line and a shaded region that represents the solution to an inequality. Let's analyze the features of the graph step by step:

1. Line Equation:

The line passes through the points $(-6, 0)$ and $(6, 6)$. We can determine the equation of the line using the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

• The slope $m$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 0}{6 - (-6)} = \frac{6}{12} = \frac{1}{2}$
• The y-intercept $b$ is where the line crosses the y-axis, which is at $b = 0$.

So, the equation of the line is: $y = \frac{1}{2}x$

2. Inequality Direction:

The shaded region is above the line. This suggests that the inequality involves values of $y$ that are greater than the line's equation. Since the line itself is included in the shaded region, the inequality is non-strict (i.e., "greater than or equal to").

Therefore, the inequality is: $y \geq \frac{1}{2}x$

Conclusion:

The inequality represented by the graph is: $y \geq \frac{1}{2}x$

Would you like more details on how the slope and intercept were determined or explanations on inequalities?

Here are 5 related questions to deepen your understanding:

1. What would the inequality look like if the region below the line was shaded?
2. How would the equation change if the line had a different slope?
3. What is the significance of the line being dashed instead of solid in graphs of inequalities?
4. How do we determine whether the inequality should be strict (>) or non-strict (≥)?
5. How would the inequality change if the line shifted vertically?

Tip: For graphing inequalities, always check whether the boundary line is included (solid line) or excluded (dashed line) to determine whether the inequality should be strict or non-strict.