Equations of parallel and perpendicular lines

Learning Objectives Identify the relationship between the slopes of parallel lines. Identify the relationship between the slopes of perpendicular lines. Write the equation of a line that is parallel to a given line and passes through a specific point. Write the equation of a line that is perpendicular to a given line and passes through a specific point. Determine if two lines are parallel, perpendicular, or neither by analyzing their equations. Apply the properties of parallel and perpendicular lines to solve geometric problems in the coordinate plane. Ever wonder how city planners design perfectly straight, non-intersecting streets or how architects ensure corners are perfect right angles? 🗺️ It's all about the geometry of parallel and perpendicular lines! This tutori...

TermDefinitionExample Parallel LinesTwo distinct lines in a coordinate plane that never intersect. They have the same steepness.The lines y = 2x + 3 and y = 2x - 1 are parallel. They both go up 2 units for every 1 unit they go to the right. Perpendicular LinesTwo lines in a coordinate plane that intersect to form a right (90°) angle.The x-axis and the y-axis are perpendicular lines. SlopeA number that measures a line's steepness, calculated as the 'rise' (vertical change) divided by the 'run' (horizontal change). It is represented by the variable 'm'.A line passing through (0,0) and (2,4) has a slope of m = (4-0)/(2-0) = 2. Slope-Intercept FormA common way to write a linear equation: y = mx + b, where 'm' is the slope and 'b' is the y...

Rule for Slopes of Parallel Lines m_1 = m_2 Two distinct, non-vertical lines are parallel if and only if their slopes are equal. To find the slope of a parallel line, simply use the same slope as the original line. Rule for Slopes of Perpendicular Lines m_1 * m_2 = -1 or m_2 = -1/m_1 Two non-vertical lines are perpendicular if and only if their slopes are opposite reciprocals. To find the slope of a perpendicular line, flip the original slope and change its sign.