Parallel lines
coplanar lines that never intersect
Parallel lines are two lines in a two-dimensional plane that never intersect, no matter how far they are extended.
Here are some important characteristics of parallel lines:
1. They have the same slope: The slope of a line is how steep it is, and it is represented by the letter “m.” Two lines are parallel if they have the same slope. For example, the line y = 2x + 3 and the line y = 2x – 1 are parallel because they both have a slope of 2.
2. They never intersect: Since parallel lines have the same slope, they can never cross each other. They will remain equidistant from each other.
3. They have different y-intercepts: The y-intercept of a line is the point where it crosses the y-axis. Two parallel lines must have different y-intercepts. For example, the line y = 2x + 3 crosses the y-axis at (0,3), while the line y = 2x + 7 crosses the y-axis at (0,7).
4. They are always the same distance apart: Parallel lines are always the same distance apart from each other. This distance is called the “distance between parallel lines.”
5. They are found in geometric shapes: Parallel lines can be found in many geometric shapes such as squares, rectangles, and parallelograms.
6. They are used in mathematics and engineering: Parallel lines have important applications in math and engineering. For example, they are used in creating accurate perspective drawings and in creating parallel circuits for electronics.
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