Parallel and Perpendicular Lines

Two lines are parallel if they have the same slope but different y-intercepts. [formula] Parallel lines never intersect. Example: y = 3x + 1 and y = 3x - 5 are parallel (both have slope 3).

Two lines are perpendicular if their slopes are negative reciprocals of each other: [formula] Perpendicular lines intersect at a 90° angle. Examples: - Slopes 2 and -frac{1}{2}: 2 times (-frac{1}{2}) = -1 ✓ perpendicular - Slopes frac{3}{4} and -frac{4}{3}: frac{3}{4} times (-frac{4}{3}) = -1 ✓ perpendicular - Slopes 3 and frac{1}{3}: 3 times frac{1}{3} = 1 neq -1 ✗ NOT perpendicular

Example: Write an equation of the line perpendicular to y = 4x + 1 that passes through (8, 3).