Key Concepts:
- Parallel Lines: Have the same slope but different y-intercepts.
- Perpendicular Lines: Have slopes that are negative reciprocals (if (m_1) is the slope, the perpendicular slope is (-\frac{1}{m_1})).
Skills Covered:
- Determining if two lines are parallel or perpendicular by comparing their slopes.
- Finding the slope of a perpendicular line given a known slope.
- Writing equations of lines that are parallel or perpendicular to a known line.
Example Problems:
- Determine if the lines (y = -\frac{2}{3}x + 4) and (2x + 3y = 6) are perpendicular.
- Find the slope of a line perpendicular to (y = \frac{4}{5}x - 3).
- Find the equation of a line parallel to (y = 3x - 7) that passes through ((2,5)).