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Given the following graph of a system of inequalities, identify the correct information below.

Which inequality is represented by line #1?

Answer 1 Question 30Choose...x < 3x > 34x + 3y ≤ −12x ≥ 34x + 3y > −12Nox ≤ 3Yes4x + 3y ≥ −12

Which inequality is represented by line #2?

Answer 2 Question 30Choose...x < 3x > 34x + 3y ≤ −12x ≥ 34x + 3y > −12Nox ≤ 3Yes4x + 3y ≥ −12

Is (2, −4) a solution to the system?

Answer 3 Question 30Choose...x < 3x > 34x + 3y ≤ −12x ≥ 34x + 3y > −12Nox ≤ 3Yes4x + 3y ≥ −12

To solve the system of inequalities represented in the graph, we need to analyze each line and the shaded regions.

### Analyzing Line #1

**Line #1** is vertical and intersects the x-axis at \(x = 3\). The region to the right of this line is shaded. This suggests the inequality:

\[ x > 3 \]

### Analyzing Line #2

**Line #2** is diagonal and has a negative slope. The line passes through the points \((-10, 10)\) and \((10, -10)\). We can calculate the slope of this line:

\[ \text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-10 - 10}{10 - (-10)} = \frac{-20}{20} = -1 \]

With a slope of \(-1\) and using the point \((10, -10)\), the equation of the line is:

\[ y = -x \]

The inequality needs to be determined based on the shaded region, which is above the line. This means:

\[ y > -x \]

### Conclusion

Based on our analysis:
- **Line #1** represents \( x > 3 \)
- **Line #2** represents \( y > -x \)

### Evaluating the Point \((2, -4)\)

We need to check if the point \((2, -4)\) satisfies both inequalities:

1. For \( x > 3 \): \( 2 > 3 \) is **False**.
2. For \( y > -x \): \(-4 > -2\) is **False**.

Therefore, the point \((2, -4)\) is **not a solution** to the system.

### Summary of Answers
1. Which inequality is represented by line #1?
   - **Answer**: \(x > 3\)

2. Which inequality is represented by line #2?
   - **Answer**: \(y > -x\)

3. Is \((2, -4)\) a solution to the system?
   - **Answer**: **No**

Would you like further clarification or have any questions about this explanation?

### Related Questions
1. How do you graph a linear inequality on a coordinate plane?
2. What does the shaded region in a graph of inequalities represent?
3. How do you determine if a point satisfies a system of inequalities?
4. What is the difference between strict and non-strict inequalities in graphs?
5. Can a system of inequalities have no solutions? If so, how can you tell from the graph?
6. How do you solve a system of linear inequalities algebraically?
7. How are inequalities used in real-world scenarios?
8. What are the implications of having parallel lines in a system of inequalities?

### Tip
When analyzing graphs of inequalities, always start by identifying the boundary lines and the regions they divide. Then use test points to determine which regions satisfy the inequalities.

Understand how to identify inequalities from graphs using line analysis and point evaluation. This detailed explanation covers analyzing lines on a coordinate plane, determining inequalities represented by specific lines, and evaluating points for solution validity. Suitable for Grades 7-9.

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