Slopes of parallel and perpendicular lines

Learning Objectives Identify the slope of a line from its equation in any form. Define the relationship between the slopes of parallel lines. Define the relationship between the slopes of perpendicular lines. Determine if two lines are parallel, perpendicular, or neither, given their equations. 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. Apply slope concepts to verify properties of geometric figures on the coordinate plane. Have you ever noticed how the streets in a city grid are perfectly parallel or intersect at perfect right angles? 🏙️ That's geometry in action, and it's all about slope! This tutorial w...

TermDefinitionExample SlopeA number that measures the 'steepness' and direction of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.A line passing through (2, 3) and (4, 7) has a slope m = (7-3)/(4-2) = 4/2 = 2. Parallel LinesTwo or more lines in a plane that never intersect. They are always the same distance apart.The opposite sides of a rectangle are parallel. Perpendicular LinesTwo lines that intersect to form a right angle (90 degrees).The x-axis and y-axis on the coordinate plane are perpendicular. Slope-Intercept FormA common way to write the equation of a line: y = mx + b, where 'm' is the slope and 'b' is the y-intercept.In the equation y = -3x + 5, the slope is -3. N...

Slope Rule for Parallel Lines If two non-vertical lines are parallel, then their slopes are equal. m_1 = m_2 Use this rule to check if two lines are parallel or to find the slope of a line that must be parallel to a given line. If the slopes are identical, the lines are parallel (assuming they have different y-intercepts). Slope Rule for Perpendicular Lines If two non-vertical lines are perpendicular, then the product of their slopes is -1. m_1 * m_2 = -1 or m_2 = -1/m_1 This means the slopes are negative reciprocals of each other. Use this rule to check if two lines are perpendicular or to find the slope of a line that must be perpendicular to a given line. Special Case: Horizontal and Vertical Lines A horizontal line (slope = 0) is perpendicular to a vertical lin...