What condition do parallel lines satisfy with regards to their slopes?

Parallel lines are lines that run in the same direction and never intersect. For two lines to be parallel in a Cartesian coordinate system, their slopes must be equal. The slope of a line is a measure of its steepness and direction, typically represented by the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

When two lines have the same slope, they maintain a consistent vertical distance apart, ensuring they do not meet at any point regardless of how far they are extended in the plane. If the slopes were different, the lines would eventually intersect at some point. Similarly, while slopes can be zero (indicating horizontal lines) or negative (indicating lines that tilt downward as one moves from left to right), these characteristics do not define parallelism in a general sense; what is crucial is the equality of the slopes, which guarantees that the lines are parallel. Therefore, the condition that parallel lines satisfy with regards to their slopes is that their slopes are equal.