Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true. Line $$ a $$ passes through $$ (-2,8) $$ and $$ (5,8) $$. Line $$ b $$ passes through $$ (2,0) $$ and $$ (4,9) $$. Line $$ c $$ passes through $$ (0,6) $$ and $$ (5,26) $$. Line $$ d $$ passes through $$ (0,8) $$ and $$ (4,7) $$.

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To determine which lines are **parallel** or **perpendicular**, we'll first calculate the **slope** of each line. The slope helps us understand the steepness and direction of a line.

### Calculating Slopes

1. **Line $$ a $$**:
   - Passes through points $$(-2, 8)$$ and $$ (5, 8) $$.
   - **Slope ($$ m_a $$)**: 
     $$
     m_a = \frac{8 - 8}{5 - (-2)} = \frac{0}{7} = 0
     $$
   - **Interpretation**: Horizontal line.

2. **Line $$ b $$**:
   - Passes through points $$ (2, 0) $$ and $$ (4, 9) $$.
   - **Slope ($$ m_b $$)**:
     $$
     m_b = \frac{9 - 0}{4 - 2} = \frac{9}{2} = 4.5
     $$

3. **Line $$ c $$**:
   - Passes through points $$ (0, 6) $$ and $$ (5, 26) $$.
   - **Slope ($$ m_c $$)**:
     $$
     m_c = \frac{26 - 6}{5 - 0} = \frac{20}{5} = 4
     $$

4. **Line $$ d $$**:
   - Passes through points $$ (0, 8) $$ and $$ (4, 7) $$.
   - **Slope ($$ m_d $$)**:
     $$
     m_d = \frac{7 - 8}{4 - 0} = \frac{-1}{4} = -0.25
     $$

### Determining Parallel Lines

**Parallel lines** have **equal slopes**.

- **Line $$ a $$ ($$ m_a = 0 $$)**: No other line has a slope of 0.
- **Line $$ b $$ ($$ m_b = 4.5 $$)**: No other line has a slope of 4.5.
- **Line $$ c $$ ($$ m_c = 4 $$)**: No other line has a slope of 4.
- **Line $$ d $$ ($$ m_d = -0.25 $$)**: No other line has a slope of -0.25.

**Conclusion**: **No lines are parallel**.

### Determining Perpendicular Lines

**Perpendicular lines** have slopes that are **negative reciprocals** of each other. This means:
$$
m_1 \times m_2 = -1
$$

Let's check each pair:

1. **Line $$ a $$ and Line $$ b $$**:
   $$
   0 \times 4.5 = 0 \neq -1 \quad \text{Not perpendicular}
   $$

2. **Line $$ a $$ and Line $$ c $$**:
   $$
   0 \times 4 = 0 \neq -1 \quad \text{Not perpendicular}
   $$

3. **Line $$ a $$ and Line $$ d $$**:
   $$
   0 \times (-0.25) = 0 \neq -1 \quad \text{Not perpendicular}
   $$

4. **Line $$ b $$ and Line $$ c $$**:
   $$
   4.5 \times 4 = 18 \neq -1 \quad \text{Not perpendicular}
   $$

5. **Line $$ b $$ and Line $$ d $$**:
   $$
   4.5 \times (-0.25) = -1.125 \neq -1 \quad \text{Not perpendicular}
   $$

6. **Line $$ c $$ and Line $$ d $$**:
   $$
   4 \times (-0.25) = -1 \quad \text{Perpendicular}
   $$

**Conclusion**: **Only Line $$ c $$ and Line $$ d $$ are perpendicular**.

### Summary

- **Parallel Lines**: **None**
- **Perpendicular Lines**: **Line $$ c $$ and Line $$ d $$**

---

**Therefore, the true statement is:**

- **Line $$ c $$ is perpendicular to Line $$ d $$.**
Line $$ c $$ is perpendicular to Line $$ d $$.

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