Find the slopes of the lines $$ l_{1} $$ and $$ l_{2} $$ defined by the two given points. Then determine whether $$ l_{1} $$ and $$ l_{2} $$ are parallel, perpendicular, or neither. $$ l_{1}:(2,0) $$ and $$ (-1,-1) $$ $$ l_{2}:(5,-4) $$ and $$ (4,-7) $$ Part: $$ 0 / 3 $$ The slope of $$ l_{1} $$ is 3

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Let's determine the slopes of lines $$ l_{1} $$ and $$ l_{2} $$ based on the given points and then analyze their relationship.

### 1. Calculating the Slope of $$ l_{1} $$

**Given Points for $$ l_{1} $$:** $$ (2, 0) $$ and $$ (-1, -1) $$.

The formula for the slope ($$ m $$) between two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Applying the formula:

$$
m_{1} = \frac{-1 - 0}{-1 - 2} = \frac{-1}{-3} = \frac{1}{3}
$$

**Slope of $$ l_{1} $$:** $$ m_{1} = \frac{1}{3} $$

*Note:* It appears there was a miscalculation in your initial assessment stating the slope of $$ l_{1} $$ is 3. The correct slope is $$ \frac{1}{3} $$.

### 2. Calculating the Slope of $$ l_{2} $$

**Given Points for $$ l_{2} $$:** $$ (5, -4) $$ and $$ (4, -7) $$.

Applying the slope formula:

$$
m_{2} = \frac{-7 - (-4)}{4 - 5} = \frac{-3}{-1} = 3
$$

**Slope of $$ l_{2} $$:** $$ m_{2} = 3 $$

### 3. Analyzing the Relationship Between $$ l_{1} $$ and $$ l_{2} $$

- **Parallel Lines:** Two lines are parallel if their slopes are equal.
  
  $$
  m_{1} = \frac{1}{3} \quad \text{and} \quad m_{2} = 3 \quad (\text{Not equal})
  $$
  
  **Conclusion:** $$ l_{1} $$ and $$ l_{2} $$ are **not parallel**.

- **Perpendicular Lines:** Two lines are perpendicular if the product of their slopes is $$ -1 $$.
  
  $$
  m_{1} \times m_{2} = \frac{1}{3} \times 3 = 1 \quad (\neq -1)
  $$
  
  **Conclusion:** $$ l_{1} $$ and $$ l_{2} $$ are **not perpendicular**.

- **Neither Parallel Nor Perpendicular:** Since neither condition above is met.

**Final Conclusion:** $$ l_{1} $$ and $$ l_{2} $$ are **neither parallel nor perpendicular**.

### **Summary**

- **Slope of $$ l_{1} $$:** $$ \frac{1}{3} $$
- **Slope of $$ l_{2} $$:** $$ 3 $$
- **Relationship:** Neither parallel nor perpendicular.
The slope of $$ l_{1} $$ is $$ \frac{1}{3} $$ and the slope of $$ l_{2} $$ is $$ 3 $$. The lines are neither parallel nor perpendicular.

Find the slopes of the lines and defined by the two given points. Then determine whether and are parallel, perpendicular, or neither.
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Part:
The slope of is 3

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Find the slopes of the lines and defined by the two given points. Then determine whether and are parallel, perpendicular, or neither. and and Part: The slope of is 3