https://file.aiquickdraw.com/mathbot/file/1726062316315x3phmdeh.jpg

The system of inequalities presented in the image is:

1. \( y < 4 - x \)
2. \( 2x - y > 2 \)
3. \( \frac{1}{4}x < y \)

Let's break this down step by step so we can help you plot the solution set on the graph.

### Step 1: Graph each inequality as a boundary line.
- **For \( y < 4 - x \):**
  - First, treat it as an equality: \( y = 4 - x \). This is a straight line with a slope of -1 and a y-intercept of 4.
  - Since it's a strict inequality (less than), the line will be **dashed**.
  - Shade the area **below** the line.

- **For \( 2x - y > 2 \):**
  - Rearrange into slope-intercept form: \( y < 2x - 2 \). The slope is 2 and the y-intercept is -2.
  - Since it's a strict inequality, graph a **dashed** line.
  - Shade the area **above** the line.

- **For \( \frac{1}{4}x < y \):**
  - Rewrite as \( y > \frac{1}{4}x \). This line has a slope of \( \frac{1}{4} \) and passes through the origin.
  - This inequality is "greater than," so the line will be **dashed**.
  - Shade the area **above** the line.

### Step 2: Find the solution region.
The solution region will be where all three shaded regions overlap.

### Step 3: Use the Mark Feature tool.
After plotting the lines and shading the appropriate regions, use the **Mark Feature** to indicate any point in the solution region where all three inequalities overlap.

Would you like further explanation on graphing these inequalities or help with the plotting process?

Here are 5 relative questions that might expand your understanding:

1. How do you determine whether to shade above or below a boundary line?
2. What is the significance of a dashed line in inequality graphs?
3. Can you always convert inequalities into slope-intercept form? Why or why not?
4. How do parallel lines affect the solution region of inequalities?
5. What happens if the solution regions of two inequalities do not overlap?

**Tip:** Always verify your shaded region by testing a point within the overlapping area to see if it satisfies all inequalities.

Use the drawing tools to form the correct answer on the grid. Graph each inequality in the system, showing the solution set as overlapping half planes:
1. y < 4 - x
2. 2x - y > 2
3. (1/4)x < y

Learn how to graph the system of linear inequalities: y < 4 - x, 2x - y > 2, and (1/4)x < y. This tutorial helps you understand the steps for shading regions and identifying overlapping solutions. Suitable for high school students in Grades 9-11.

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