parallel lines
two lines that never intersect
Parallel lines are two lines that never intersect no matter how long they are extended in either direction. The term parallel is derived from the Greek word parallelos which means alongside one another.
To determine if two lines are parallel, we examine their slopes which indicate the steepness of the lines. If the slopes of two lines are equal, then the lines are parallel.
For example, consider the equations:
y = 2x + 1
y = 2x + 4
Both lines have a slope of 2 which means they are parallel. This can be visually confirmed by observing that the lines have the same steepness and do not intersect no matter how long they are extended in either direction.
It is important to note that if two lines are not parallel, they will either intersect at a point or be skew lines (lines in different planes that do not intersect but also are not parallel).
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