explain how to identify if 2 lines are parallel orperpendicular based on their slopes

To determine if two lines are **parallel** or **perpendicular** based on their slopes, you can follow these guidelines:

### 1. Identifying Parallel Lines

Two lines are **parallel** if they have the **same slope**. 

- If the slope of the first line is \( m_1 \) and the slope of the second line is \( m_2 \), then the lines are parallel if:

\[
m_1 = m_2
\]

Parallel lines will never intersect because they have the same steepness and direction.

### 2. Identifying Perpendicular Lines

Two lines are **perpendicular** if the product of their slopes is **-1**.

- If the slope of the first line is \( m_1 \) and the slope of the second line is \( m_2 \), then the lines are perpendicular if:

\[
m_1 \times m_2 = -1
\]

Alternatively, one slope is the **negative reciprocal** of the other. This means if one line has a slope of \( m_1 \), the other line must have a slope of \( -\frac{1}{m_1} \) to be perpendicular.

For example:
- If one line has a slope of \( 2 \) (i.e., \( m_1 = 2 \)), the slope of a line perpendicular to it would be \( -\frac{1}{2} \) (i.e., \( m_2 = -\frac{1}{2} \)).

Perpendicular lines intersect at a 90-degree angle.

Would you like more examples, or do you have any questions?

Here are 5 relative questions for you:

1. How do you find the slope of a line given two points?
2. What happens to the slopes of two parallel lines if they are both rotated by 90 degrees?
3. Can two lines with different y-intercepts be parallel?
4. How can you determine if two lines are neither parallel nor perpendicular based on their slopes?
5. What does it mean if the product of the slopes of two lines is positive but not equal to 1?

**Tip:** To quickly check for perpendicularity, remember that flipping a slope and changing its sign gives you the slope of a perpendicular line.

Learn how to determine if two lines are parallel or perpendicular based on their slopes. Understand the conditions where lines have the same slope for parallelism and the product of slopes being -1 for perpendicularity. Suitable for high school students studying geometry and lines.

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