https://file.aiquickdraw.com/mathbot/file/1725902640041sxijq7ov.jpg

The shaded region of the graph represents the solution to an inequality.   



Find the inequality represented in the graph.

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?

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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.

The shaded region of the graph represents the solution to an inequality. Find the inequality represented in the graph.

Learn how to find the inequality represented by a shaded region in a graph. This problem involves key algebraic concepts such as linear inequalities, slope-intercept form, and graphing. Suitable for students in Grades 8-10.

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