https://file.aiquickdraw.com/mathbot/file/1730698546785ddjyrlxh.jpg

To find the inequality representing this graph, let's analyze it step-by-step.

1. **Identify the Line**: 
   - The line appears to pass through points \((-8, -4)\) and \((0, 0)\).
   
2. **Calculate the Slope**: 
   - Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
   - Using points \((-8, -4)\) and \((0, 0)\):
     \[
     m = \frac{0 - (-4)}{0 - (-8)} = \frac{4}{8} = \frac{1}{2}
     \]

   So, the slope of the line is \( \frac{1}{2} \).

3. **Find the Equation of the Line**:
   - Using the slope \( \frac{1}{2} \) and the y-intercept at \( (0, 0) \), the equation of the line is:
     \[
     y = \frac{1}{2}x
     \]

4. **Determine the Inequality Symbol**:
   - The shaded region is above the line, which suggests a "greater than" inequality.
   - Since the line is solid, it includes points on the line, meaning we use "greater than or equal to."

5. **Final Inequality**:
   - The inequality in slope-intercept form is:
     \[
     y \geq \frac{1}{2}x
     \]

### Answer
The inequality that represents this graph is:
\[
y \geq \frac{1}{2}x
\]

Would you like more details, or do you have any questions?

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**Related Questions**:

1. How would the inequality change if the shaded area were below the line?
2. What if the line were dashed instead of solid—how would that affect the inequality?
3. How can you verify which side of the line represents the solution to the inequality?
4. How does changing the slope affect the position of the shaded region?
5. What are the steps to determine the equation of a line in general?

**Tip**: Always check the shading to determine whether to use \( \geq, \leq, >,\) or \(<\) in inequalities.

This is the graph of a linear inequality. Write the inequality in slope-intercept form.

Learn how to write a linear inequality in slope-intercept form based on a graph. This example involves identifying the slope and y-intercept from a graphed line, and determining the appropriate inequality symbol based on shading. Suitable for students in Grades 7-9.

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