https://file.aiquickdraw.com/mathbot/file/17284162873003c7w4qim.jpg

The graph shows a linear inequality. From the image, we can break the problem down as follows:

1. **Identify the boundary line**: The line appears to pass through two points:
   - \( (-5, 3) \)
   - \( (2, 1) \)

   To find the equation of the line, we calculate the slope (m):

   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{2 - (-5)} = \frac{-2}{7}
   \]

   So, the slope \( m = -\frac{2}{7} \).

   Using the point-slope form of the line \( y - y_1 = m(x - x_1) \), let's use the point \( (2, 1) \):

   \[
   y - 1 = -\frac{2}{7}(x - 2)
   \]

   Simplifying:

   \[
   y - 1 = -\frac{2}{7}x + \frac{4}{7}
   \]

   \[
   y = -\frac{2}{7}x + \frac{4}{7} + 1
   \]

   \[
   y = -\frac{2}{7}x + \frac{11}{7}
   \]

2. **Determine the inequality**: The shaded region is below the line, which suggests that the inequality is \( \leq \) or \( < \). Since the boundary line is solid, the inequality is \( \leq \).

Thus, the inequality represented by the graph is:

\[
y \leq -\frac{2}{7}x + \frac{11}{7}
\]

Would you like further details or have any questions?

### 5 Related Questions:
1. How do you graph an inequality with a non-solid boundary line?
2. Can an inequality have more than one shaded region?
3. What happens when an inequality flips its sign (e.g., from \( \leq \) to \( \geq \)) in a graph?
4. How does changing the slope affect the graph of a linear inequality?
5. What is the significance of testing points to determine the correct shaded region?

### Tip:
Always test a point (like \( (0, 0) \), if not on the line) to verify which side of the line should be shaded when graphing inequalities.

Find the inequality represented by the graph.

Learn how to find the inequality represented by a graph. This problem involves understanding linear inequalities, graphing techniques, and using slope-intercept form to determine the equation of a line. Suitable for students in Grades 8-10.

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