What is the defining characteristic of parallel lines?

The defining characteristic of parallel lines is that they have the same slope and never intersect. In the context of a coordinate plane, parallel lines maintain a constant distance from each other, which is a direct result of having identical slopes. This means that no matter how far you extend them in either direction, they will never meet; they will always remain equidistant.

Parallel lines can be horizontal, vertical, or slanted at any angle, as long as their slopes are equal. This characteristic is crucial in various areas of mathematics, including geometry and calculus, as it informs the relationships and angles formed by lines in different geometric configurations. The concept of slopes being equal ensures that when you graph the lines, they will overlay in a way that visually demonstrates their parallel nature.