https://file.aiquickdraw.com/mathbot/file/1729331026873oglwysyj.jpg

https://file.aiquickdraw.com/mathbot/file/1729331026873znp5qssu.jpg

The system of inequalities shown in the images is:

\[
y \geq -\frac{7}{4}x + 4
\]
\[
y < \frac{1}{4}x - 4
\]

### Steps to match the graph:

1. **Graph the first inequality**: \( y \geq -\frac{7}{4}x + 4 \)
   - The line \( y = -\frac{7}{4}x + 4 \) has a **slope** of \(-\frac{7}{4}\) and a **y-intercept** of 4.
   - Since the inequality is \( \geq \), the shading should be **above** the line, and the line should be **solid**.

2. **Graph the second inequality**: \( y < \frac{1}{4}x - 4 \)
   - The line \( y = \frac{1}{4}x - 4 \) has a **slope** of \( \frac{1}{4} \) and a **y-intercept** of \(-4\).
   - Since the inequality is \( < \), the shading should be **below** the line, and the line should be **dashed**.

Now, to choose the correct graph:
- Look for a graph where one line is **solid** and has a steep negative slope, and another line is **dashed** with a gentler positive slope.
- The shading should be **above** the solid line and **below** the dashed line.

Based on the description, select the graph that satisfies these conditions.

Do you want more details or have any questions?

Here are 5 related questions:
1. How do you determine which side of a line to shade for an inequality?
2. How do solid and dashed lines differ when graphing inequalities?
3. What is the significance of the slope and y-intercept in graphing a linear equation?
4. How would the graph change if the inequalities were reversed (e.g., \( y \leq \) instead of \( y \geq \))?
5. What methods can you use to check if a point satisfies both inequalities?

**Tip:** Always test a point (like \( (0, 0) \)) to see if it lies in the shaded region!

Choose the graph that corresponds to the given system of inequalities: y ≥ (-7/4)x + 4 and y < (1/4)x - 4.

Learn how to graph a system of linear inequalities, including y ≥ (-7/4)x + 4 and y < (1/4)x - 4. Understand how to shade regions above and below lines and distinguish between solid and dashed lines. Suitable for high school students in Grades 9-12.

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