1. Parallel, Perpendicular, Horizontal, and Vertical Lines
Geometry 3-6
Parallel, Perpendicular, Horizontal, and Vertical Lines

2. Two Special Lines Horizontal lines: y = number
Vertical lines: x = number

3. Examples Vertical line through (2,4) Horizontal line through (3,-5)
A line through (2,3) and (5,3)

4. 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

5. 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

6. 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

7. 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