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Parallel and Perpendicular Lines in the Cartesian Plane. Stereotypes about Parallel and Perpendicular Lines. They are boring! They have no use in life . Just a series of lines with positive slopes… No Big Deal. Color coded to show parallel and perpendicular lines. WHOA!.
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Stereotypes about Parallel and Perpendicular Lines They are boring! They have no use in life.
Parallel and Perpendicular Lines are Everywhere Maps Construction Artwork Sports
Review:SlopeInterceptForm y = mx + b m is the slope of the line bis the y-intercept Life is easy when you’re in slope intercept form
y -intercept • y = mx + b • The y-intercept is the y value when x = 0. • Visually, the y-intercept is y value when the line crosses the y axis • http://www.mathsisfun.com/data/function-grapher.php
Slope y = mx + b Slope Slider Slope ofvertical lines?
Identifying the Slope and the y-intercept • 3y = 6x + 9 • 5y = 10x • y = -1 • x = 3 Hint
Review: Finding the Equation of the Line given a Slope and a Point on the Line • y = mx + b • Given the slope, m, and a point, (x , y), then we can find b, the y-intercept. • b = y – mx • Once we find b, we can find the equation of the line.
Practice: Finding the Equation of the Line given the Slope and a Point on the Line • p = (-2 , 2) m = 4p = (-3 , 4) m = -2p = (-2 , 2/3) m = -4/3
Graphing Activity • 1. Graph line segments. • Be sure that each endpoint is an integer coordinate, such as (1,3) or (-3,0)Compute and record their slope. • 2. Then graph a parallel line to each of the three line segments. Compute and record the slopes of the parallel lines. Then delete the parallel lines. • 3. Then graph a perpendicular line to each of the three line segments. Compute and record the slopes of the perpendicular lines.
Find the Slope of a Parallel Line • y = (1/3)x + 2 • y – 1 = 6x • 2y = 5x + 3 • 4y = 8x • y = 6 • x = -3
Find the Slope of a Perpendicular Line • y = -3x – 2 • y = (1/3)x + 2 • y – 1 = 6x • 2y = 5x + 3 • y = 6 • x = -3
Find the Equation of the Parallel Line that passes through the Given Point. • y = (1/3)x + 2 , p = (2 , -3) • 2y = 5x + 3 , p = (1/2 , 2/3) • y = 6 , p = (6 , 0) • x = -3 , p = (1 , 2)
Find the Equation of the Perpendicular Line that passes through the Given Point. y = -3x – 2 , p = (-1 , 4) 4y = 8x , p = (1 , 1/3) y = 6 , p = (6 , 0) x = -3 , p = (1 , 2)