To determine whether two lines are parallel or perpendicular, you need to analyze their slopes. The slope of a line represents how steep the line is, and it is usually denoted by the letter $m$.

1. Identifying Parallel Lines

Two lines are parallel if they have the same slope and are not the same line. This means that the lines will never intersect.

• For example, if you have two lines with equations: $y = m_1x + b_1$ $y = m_2x + b_2$ The lines are parallel if: $m_1 = m_2$

2. Identifying Perpendicular Lines

Two lines are perpendicular if the product of their slopes is -1. This means that one line's slope is the negative reciprocal of the other. When lines are perpendicular, they intersect at a right angle (90 degrees).

• For example, if you have two lines with equations: $y = m_1x + b_1$ $y = m_2x + b_2$ The lines are perpendicular if: $m_1 \times m_2 = -1$

Special Cases:

• Horizontal and Vertical Lines: A horizontal line has a slope of 0, and a vertical line has an undefined slope. These lines are always perpendicular to each other.

Would you like more details on this topic or have any questions?

Relative Questions:

1. How can you find the slope of a line given two points?
2. What happens when two lines have the same slope and the same y-intercept?
3. How can you determine if two lines are neither parallel nor perpendicular?
4. What is the relationship between slopes of perpendicular lines on a coordinate plane?
5. How do you find the equation of a line parallel or perpendicular to a given line?

Tip:

Always double-check the slopes when determining if lines are parallel or perpendicular. Even a small mistake in calculating the slope can lead to incorrect conclusions.