To determine whether two lines are parallel, perpendicular, or neither, you can look at their slopes if you have the equations in slope-intercept form (y = mx + b).
1. Parallel Lines:
Two lines are parallel if they have the same slope. For example, if you have two lines with equations y = 2x + 3 and y = 2x – 1, both lines have a slope of 2, so they are parallel.
2. Perpendicular Lines:
Two lines are perpendicular if the product of their slopes equals -1. This means that if one line has a slope of m1, the other line should have a slope of m2 where m1 * m2 = -1. For example, if one line has a slope of 3, a line perpendicular to it would have a slope of -1/3.
3. Neither:
If the lines do not meet the criteria for being parallel or perpendicular (same slope or product of slopes equaling -1), then they are classified as neither. For instance, if one line has a slope of 2 and another has a slope of 1, they are neither parallel nor perpendicular.
In summary, compare the slopes of the lines to determine their relationship:
- Same slope = Parallel
- Product of slopes = -1 = Perpendicular
- Otherwise = Neither