Question

Parallel lines are straight lines in a plane that never intersect and have the same slope, meaning they maintain a constant distance apart. Perpendicular lines, on the other hand, intersect at a right angle (90 degrees), creating a relationship characterized by their slopes being negative reciprocals of each other.

Answer 1

That's a great summary of the characteristics of parallel and perpendicular lines!

To elaborate a bit more:

**Parallel Lines:**
- In a coordinate plane, if two lines are described by the equations \(y = mx + b_1\) and \(y = mx + b_2\) (where \(m\) is the slope and \(b_1\) and \(b_2\) are the y-intercepts), they are parallel because they have the same slope \(m\) but different y-intercepts.
- As a result, they never meet, regardless of how far they are extended.

**Perpendicular Lines:**
- Two lines are perpendicular if the product of their slopes is \(-1\). If one line has a slope of \(m\), the slope of a line perpendicular to it will be \(-\frac{1}{m}\).
- For example, if one line has a slope of \(2\), a line perpendicular to it would have a slope of \(-\frac{1}{2}\).
- This relationship ensures that the two lines will intersect at a right angle (90 degrees).

Understanding these properties is crucial in various areas of geometry and algebra, as they help to determine relationships between different lines and shapes in a plane.