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 lines.

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Parallel and perpendicular lines in the cartesian plane

  1. 1. Parallel and Perpendicular Lines in the Cartesian Plane<br />
  2. 2. Stereotypes about Parallel and Perpendicular Lines<br />They are boring!<br />They have no use in life.<br />
  3. 3. Just a series of lines with positive slopes…No Big Deal<br />
  4. 4. Color coded to show parallel and perpendicular lines<br />
  5. 5. WHOA!<br />
  6. 6. I know… I’m Awesome!<br />
  7. 7. Parallel and Perpendicular Lines are Everywhere <br />Maps<br />Construction<br />Artwork<br />Sports<br />
  8. 8. Review:SlopeInterceptForm<br />y = mx + b<br />m is the slope of the line<br />bis the y-intercept<br />Life is easy when you’re in slope intercept form<br />
  9. 9. y -intercept<br />y = mx + b<br />The y-intercept is the y value when x = 0.<br />Visually, the y-intercept is y value when the line crosses the y axis<br />http://www.mathsisfun.com/data/function-grapher.php<br />
  10. 10. Slope<br />(𝑥2,𝑦2)<br /> <br />y = mx + b<br />Slope Slider<br />Slope ofvertical lines?<br />(𝑥1,𝑦1)<br /> <br />
  11. 11. Identifying the Slope and the y-intercept<br />3y = 6x + 9<br />5y = 10x<br />y = -1<br />x = 3<br />Hint<br />
  12. 12. Review: Finding the Equation of the Line given a Slope and a Point on the Line<br />y = mx + b<br />Given the slope, m, and a point, (x , y), then we can find b, the y-intercept. <br />b = y – mx<br />Once we find b, we can find the equation of the line.<br />
  13. 13. Practice: Finding the Equation of the Line given the Slope and a Point on the Line<br />p = (-2 , 2) m = 4p = (-3 , 4) m = -2p = (-2 , 2/3) m = -4/3<br />
  14. 14. Graphing Activity<br />1. Graph line segments. <br />Be sure that each endpoint is an integer coordinate, such as (1,3) or (-3,0)Compute and record their slope.<br />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. <br />3. Then graph a perpendicular line to each of the three line segments. Compute and record the slopes of the perpendicular lines. <br />
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  18. 18. Parallel Lines<br />
  19. 19. Find the Slope of a Parallel Line<br />y = (1/3)x + 2 <br />y – 1 = 6x<br />2y = 5x + 3<br />4y = 8x<br />y = 6<br />x = -3<br />
  20. 20. Perpendicular Lines<br />
  21. 21. Find the Slope of a Perpendicular Line<br />y = -3x – 2<br />y = (1/3)x + 2 <br />y – 1 = 6x<br />2y = 5x + 3<br />y = 6<br />x = -3<br />
  22. 22. Find the Equation of the Parallel Line that passes through the Given Point.<br />y = (1/3)x + 2 , p = (2 , -3) <br />2y = 5x + 3 , p = (1/2 , 2/3)<br />y = 6 , p = (6 , 0) <br />x = -3 , p = (1 , 2)<br />
  23. 23. Find the Equation of the Perpendicular Line that passes through the Given Point.<br />y = -3x – 2 , p = (-1 , 4)<br />4y = 8x , p = (1 , 1/3)<br />y = 6 , p = (6 , 0) <br />x = -3 , p = (1 , 2)<br />

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