Download Algebra II 2-4

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