Question
What makes a line parallel?
Answers
GPT-4o mini
Two lines are considered parallel if they are in the same plane and never intersect, no matter how far they are extended in either direction. In mathematical terms, parallel lines have the same slope when expressed in a Cartesian coordinate system. This means that if you have two lines in the slope-intercept form, \(y = mx + b\), where \(m\) represents the slope, the lines are parallel if their slopes (\(m\)) are identical.
For example:
- Line 1: \(y = 2x + 3\) (slope = 2)
- Line 2: \(y = 2x - 5\) (slope = 2)
Because both lines have a slope of 2, they are parallel.
Additionally, in a geometric context, parallel lines will maintain a constant distance from each other and will not meet.
For example:
- Line 1: \(y = 2x + 3\) (slope = 2)
- Line 2: \(y = 2x - 5\) (slope = 2)
Because both lines have a slope of 2, they are parallel.
Additionally, in a geometric context, parallel lines will maintain a constant distance from each other and will not meet.