https://file.aiquickdraw.com/mathbot/file/1728413946487t6bms070.jpg

You have uploaded an image containing linear inequalities, asking for the graphs of each. Let's go through each inequality and how to graph them step by step.

### To graph the inequalities:
1. **Convert each inequality into an equation by replacing the inequality symbol with an equal sign to find the boundary line.**
2. **Determine whether the line is solid or dashed:**
   - If the inequality is "≤" or "≥", the line is solid.
   - If the inequality is "<" or ">", the line is dashed.
3. **Shade the correct region:**
   - For "≥" or ">", shade above the line.
   - For "≤" or "<", shade below the line.

### Let's analyze the inequalities one by one:

1. **Inequality**: \( y < -\frac{4}{3}x - 3 \)
   - **Boundary line**: \( y = -\frac{4}{3}x - 3 \) (dashed line since it's "<").
   - **Shade**: Below the line because it's "<".

2. **Inequality**: \( y \leq -x - 1 \)
   - **Boundary line**: \( y = -x - 1 \) (solid line since it's "≤").
   - **Shade**: Below the line because it's "≤".

3. **Inequality**: \( y \leq -\frac{1}{5}x + 2 \)
   - **Boundary line**: \( y = -\frac{1}{5}x + 2 \) (solid line since it's "≤").
   - **Shade**: Below the line because it's "≤".

4. **Inequality**: \( y > \frac{4}{5}x - 3 \)
   - **Boundary line**: \( y = \frac{4}{5}x - 3 \) (dashed line since it's ">").
   - **Shade**: Above the line because it's ">".

5. **Inequality**: \( y \leq -2x + 3 \)
   - **Boundary line**: \( y = -2x + 3 \) (solid line since it's "≤").
   - **Shade**: Below the line because it's "≤".

6. **Inequality**: \( y \geq -\frac{7}{5}x - 4 \)
   - **Boundary line**: \( y = -\frac{7}{5}x - 4 \) (solid line since it's "≥").
   - **Shade**: Above the line because it's "≥".

7. **Inequality**: \( y \geq -\frac{2}{5}x - 1 \)
   - **Boundary line**: \( y = -\frac{2}{5}x - 1 \) (solid line since it's "≥").
   - **Shade**: Above the line because it's "≥".

8. **Inequality**: \( y \geq \frac{3}{5}x \)
   - **Boundary line**: \( y = \frac{3}{5}x \) (solid line since it's "≥").
   - **Shade**: Above the line because it's "≥".

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Would you like me to generate the graphs for you, or explain any further details? Here are 5 related questions to consider:

1. How can you determine the slope of the line from each inequality?
2. What is the significance of the y-intercept in graphing linear inequalities?
3. How would a system of inequalities be graphed when multiple lines overlap?
4. How does changing the slope affect the angle of the line in the graph?
5. How would these inequalities change if we used a different sign, like ">" or "≥"?

**Tip:** Always test a point (like \( (0, 0) \)) to verify which region should be shaded if you're unsure.

Sketch the graph of each linear inequality from the given image.

Learn how to graph linear inequalities such as y ≤ -x - 1 and y ≥ 7/5x - 4. This step-by-step guide covers how to plot boundary lines, determine shading regions, and analyze linear inequalities using slope-intercept form. Ideal for students in Grades 8-10.

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