https://file.aiquickdraw.com/mathbot/file/1728526898916836lvv2u.jpg

In this image, we have two graphs showing linear inequalities that we need to express in slope-intercept form. Let's break down each graph:

### Left Graph:
1. **Identifying the slope and y-intercept:**
   - The dashed line indicates that the inequality is either \(<\) or \(>\), meaning the boundary is not included.
   - The line crosses the y-axis at \(y = 8\), so the **y-intercept** is \(8\).
   - The line has a negative slope. To calculate the slope, we can use the points \((0, 8)\) and \((4, 0)\).
     \[
     \text{slope} = \frac{0 - 8}{4 - 0} = \frac{-8}{4} = -2
     \]
   - The inequality seems to shade below the line, so the inequality will be \(y < -2x + 8\).

   **Answer:** \( y < -2x + 8 \)

### Right Graph:
1. **Identifying the slope and y-intercept:**
   - The solid line indicates that the inequality is either \( \leq \) or \( \geq \), meaning the boundary is included.
   - The line crosses the y-axis at \(y = -2\), so the **y-intercept** is \(-2\).
   - The slope is positive. Using the points \((0, -2)\) and \((2, 2)\), we calculate:
     \[
     \text{slope} = \frac{2 - (-2)}{2 - 0} = \frac{4}{2} = 2
     \]
   - The shading is above the line, so the inequality is \(y \geq 2x - 2\).

   **Answer:** \( y \geq 2x - 2 \)

### Final Inequalities:
- Left graph: \( y < -2x + 8 \)
- Right graph: \( y \geq 2x - 2 \)

Would you like further details on how these inequalities were derived or have any other questions? 

Here are some related questions:
1. How do you determine if a line should use \(<\), \(>\), \( \leq \), or \( \geq \)?
2. What does the slope of a line represent in terms of the graph?
3. Why do we check the shading to determine the direction of the inequality?
4. How can you find the slope of a line using two points?
5. What changes if the inequality symbol is flipped (e.g., from \( < \) to \( \leq \))?

**Tip:** Remember that the type of line (solid or dashed) tells you whether the boundary is included in the inequality!

Write the inequality shown on each graph (in slope-intercept form).

Learn how to write linear inequalities in slope-intercept form from a graph. This problem includes finding the slope, determining the inequality sign, and analyzing shading for solutions. Suitable for students in Grades 8-10.

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