Geometry 3-6

Parallel, Perpendicular, Horizontal, and Vertical Lines

Two Special Lines

• Horizontal lines: y = number

• Vertical lines: x = number

Examples

• Vertical line through (2,4)

• Horizontal line through (3,-5)

• A line through (2,3) and (5,3)

Definitions

• Parallel lines- two lines that never intersect– Parallel lines have equal slopes

• Perpendicular lines- two lines that intersect at a common point and create 90 degree angles– Perpendicular lines have opposite reciprocal

slopes

Examples

Parallel lines: (same slope)y = 2x – 1 and y = 2x + 9y = -2/3x -1 and y = -2/3x – 3

Perpendicular lines: (opposite reciprocal)y = 3x + 1 and y = -1/3x + 1y = -4/5x – 2 and y = 5/4x + 5

Example

• Write a line in slope-intercept form that is parallel to y = 1.5x + 6 and through (4,5)

• Parallel line means: m = 1.5y = mx + b5 = 1.5(4) + b substitute x and y values5 = 6 + b multiplyb = -1 subtract 6 from each sidey = 1.5x – 1 substitute b into the equation

Example

• Write the equation of a line perpendicular to y = -3/4x + 2 and through (6,-4)

• Perpendicular means: m = 4/3y = mx + b-4 = (4/3)(6) + b substitute x and y values-4 = 8 + b multiply-12 = b subtract 8 from each sidey = (4/3)x – 12 substitute b into equation