Final answer:
To determine if lines are parallel, perpendicular, or neither, compare their slopes. Parallel lines have the same slope, perpendicular lines have negative reciprocal slopes, and lines with different slopes are neither parallel nor perpendicular.
Step-by-step explanation:
In order to determine whether lines are parallel, perpendicular, or neither, we can look at the slopes of the lines. If two lines have the same slope, they are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular. If the slopes are different but not negative reciprocals, then the lines are neither parallel nor perpendicular.
For example, consider the lines y = 2x + 3 and y = -1/2x + 4. The slopes of these lines are 2 and -1/2, which are not the same but are negative reciprocals. Thus, the lines are perpendicular to each other.
Another example would be the lines y = 3x + 2 and y = 4x + 5. The slopes of these lines are both 3, so they are parallel to each other.