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.
and
and
Part:
The slope of is 3

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1. Calculating the Slope of

2. Calculating the Slope of

3. Analyzing the Relationship Between and

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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