In coordinate geometry, the concept of slope plays a crucial role in determining the relationship between two lines. Slope can be defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on a line. It is denoted by the letter 'm' and represents the steepness of a line.

To determine whether two lines are parallel, we compare their slopes. If the slopes are equal, the lines are parallel. Conversely, if the slopes are different, the lines are not parallel. For example, consider two lines with slopes of 2 and -2. Since these slopes are not equal, the lines are not parallel.

Determining whether two lines are perpendicular is slightly different. When two lines are perpendicular, the product of their slopes is always -1. For instance, if one line has a slope of 3, the perpendicular line will have a slope of -1/3.

Remember, parallel lines have equal slopes, while perpendicular lines have slopes that are negative reciprocals of each other. Use this understanding to solve problems involving parallel and perpendicular lines!