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Parallel and perpendicular lines in the cartesian plane
 

Parallel and perpendicular lines in the cartesian plane

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The slide show review slope intercept form and provides instruction for a constructivist activity for students to discover the relationship between the slopes of two parallel or two perpendicular ...

The slide show review slope intercept form and provides instruction for a constructivist activity for students to discover the relationship between the slopes of two parallel or two perpendicular lines.

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    Parallel and perpendicular lines in the cartesian plane Parallel and perpendicular lines in the cartesian plane Presentation Transcript

    • 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!
    • I know… I’m Awesome!
    • 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
      (𝑥2,𝑦2)
       
      y = mx + b
      Slope Slider
      Slope ofvertical lines?
      (𝑥1,𝑦1)
       
    • 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.
    • Parallel 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
    • Perpendicular Lines
    • 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)