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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 + 9 y = -2/3x -1 and y = -2/3x – 3 Perpendicular lines: (opposite reciprocal) y = 3x + 1 and y = -1/3x + 1 y = -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 = 1.5 y = mx + b 5 = 1.5(4) + b substitute x and y values 5=6+b multiply b = -1 subtract 6 from each side y = 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 = 4/3 y = mx + b -4 = (4/3)(6) + b substitute x and y values -4 = 8 + b multiply -12 = b subtract 8 from each side y = (4/3)x – 12 substitute b into equation