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Parallel and Perpendicular Lines in the Cartesian Plane

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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Parallel and Perpendicular Lines in the Cartesian Plane

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  1. Parallel and Perpendicular Lines in the Cartesian Plane

  2. Stereotypes about Parallel and Perpendicular Lines They are boring! They have no use in life.

  3. Just a series of lines with positive slopes…No Big Deal

  4. Color coded to show parallel and perpendicular lines

  5. WHOA!

  6. I know… I’m Awesome!

  7. Parallel and Perpendicular Lines are Everywhere Maps Construction Artwork Sports

  8. 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

  9. 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

  10. Slope y = mx + b Slope Slider Slope ofvertical lines?

  11. Identifying the Slope and the y-intercept • 3y = 6x + 9 • 5y = 10x • y = -1 • x = 3 Hint

  12. 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.

  13. 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

  14. 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.

  15. Parallel Lines

  16. Find the Slope of a Parallel Line • y = (1/3)x + 2 • y – 1 = 6x • 2y = 5x + 3 • 4y = 8x • y = 6 • x = -3

  17. Perpendicular Lines

  18. 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

  19. 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)

  20. 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)

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