How to Write Equations of Parallel and Perpendicular Lines Definition, Types, Examples & Uses

How to Write Equations of Parallel and Perpendicular Lines

Subject: Mathematics

Book: Maths Mastery

Two lines are parallel if they share the same slope but have different y-intercepts (m₁ = m₂). Perpendicular lines’ slopes are negative reciprocals (m₁ × m₂ = –1). For instance, if a line has slope 2, a parallel line also has slope 2, while a perpendicular line’s slope is –1/2. In slope-intercept form y = mx + b, changing b shifts the line parallelly, and switching to the negative reciprocal changes its orientation to perpendicular. In fields like architecture or geometry proofs, this concept ensures accurate angle construction and parallel design alignment. Practice with slope forms cements your ability to interpret and create consistent geometric relationships.