https://file.aiquickdraw.com/mathbot/file/1725828197296hrsof3y3.jpg

The inequality given in the image is \( y \leq -\frac{3}{4}x + 5 \).

### Steps to graph the inequality:
1. **Plot the boundary line**: The equation of the boundary line is \( y = -\frac{3}{4}x + 5 \). Since the inequality is \( \leq \), the boundary line will be solid, meaning that points on the line are included in the solution.
   
   - The slope is \( -\frac{3}{4} \), so for every 4 units you move to the right, you go down by 3 units.
   - The y-intercept is 5, so the line crosses the y-axis at \( (0, 5) \).

2. **Shade the region**: Since the inequality is \( y \leq -\frac{3}{4}x + 5 \), you will shade the area below the line, where the y-values are less than or equal to the line.

### Key Points:
- Start at \( (0, 5) \) on the y-axis.
- Move according to the slope: down 3 and right 4 to plot additional points like \( (4, 2) \) or \( (-4, 8) \).
- Draw the solid line through these points.
- Shade below the line.

Do you need further details on any part of this? Let me know! Here are some follow-up questions:

1. Why is the line solid instead of dashed?
2. How do you determine which side of the line to shade?
3. What does the slope \( -\frac{3}{4} \) represent in the context of this inequality?
4. How would the graph change if the inequality were \( y > -\frac{3}{4}x + 5 \)?
5. Can you find the x-intercept of the boundary line?

**Tip:** Always remember that if the inequality sign is \( \leq \) or \( \geq \), the boundary line should be solid, while for \( < \) or \( > \), the line should be dashed.

Learn how to graph the linear inequality y ≤ -3/4x + 5 with a step-by-step approach. Understand key concepts like slope, y-intercept, and shading regions based on inequalities. Suitable for students in Grades 8-10.

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