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Slope Intercept

Slope Intercept

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Slope Intercept

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  1. Slope Intercept EDTE 203

  2. 8th Grade Algebra Natasha Bolen

  3. Table of Contents • Introduction • Essential Question • Background *History *Solving Slope *Solving Slope given 2 points on a line *Being able to graph a line with the points and slope *Recognizing Slope and how to graph a line that’s in slope intercept form. *Being able to recognize when an xy table is useful. *Real Life Applications • Assessment

  4. Introduction

  5. What Will You Learn in This Lesson • A student will learn easier ways of identifying slope in an equation. • A student will be able to recognize how slope is important in everyday life.

  6. Essential Question What makes understanding slope beneficial to your everyday life?

  7. Background How Does Slope Roll?

  8. History of Slope Intercept • Question 1: Why does “m” represent slope? • Answer: Many think the letter “m” comes from the French word “mentor”, which means to climb!

  9. History of Slope Con. • Question 2: When was the earliest print of “m” being used to represent slope? • Answer: The earliest known example of the “m” was in a text book by O’Brien in 1844. • Answer2: Another example of this was in Webster’s Dictionary in 1909.

  10. History of Slope Con. • Question 3: How do other countries represent slope? • Answer: Sweden “k” Netherlands “a”, “p”, or “m” Austria: “k”

  11. Solving Slope • Calculate slope by given 2 points on a line. • Recognizing slope when an equation is in slope intercept form. • Make an xy table and be able to recognize how those finding correlate with slope and how to graph a line.

  12. What If you’re Given 2 Points? • Question: What is the slope of the line containing the points (-1,2) and (3,4)? • You have to use the equation for finding slope which is m= change in y change in x

  13. You can also look at this equation and think of it as: m= y2-y1 x2-x1 so lets try it using the points (-3,-6) and (0,-4)? m= -4-(-6) = 2 = rise 0-(-3) 3 run

  14. What if you had to graph that line? • So now you are given two points on the line (-3,-6) and (0,-4) and you are given the slope of 2/3. • What you do is graph one of the points and use the slope from there rising up 2 and running over 3.

  15. What if you were given the equation of a line? • Lets say you were given the equation y=-2x+3. • This is in slope intercept form! Y = mx + b / Y = -2x + 3 Where -2 is m and 3 is the y intercept (b). *remember that y intercept is where it crosses on the y axis (vertical)!!

  16. So How do you graph a line just given this information? • First you have to plot the point (0,3) and then rise -2 and run 1.

  17. How does making an xy table help? • What if you were given an equation that looked like this…. y - 2 = 3/2x – 1…this doesn’t look so easy to graph right away! So you need to make an xy table.

  18. Making an XY Table y - 2 = 3/2x – 1 X Y 0 1 2 4 -2 -2

  19. Real Life Applications • Climbing a mountain • Ramps for the handicapped • An airplane taking off and landing • A slide • A roof of a house • Skiing down a hill

  20. Music and Slope • This song is a fun way to memorize slope intercept form!! • Click on the musical note to listen to it.

  21. Games on Slope • Click on the icon to your right to play a game on identifying slope!

  22. Assessment

  23. Learning Contract • You must earn a total of 40 points. The boxes that are highlighted in yellow are cumpolsory (required) and are worth a total of 20 points. • Knowing/understanding: 4 points • Apply/Analyze: 6 points • Create/Evaluate: 8 points

  24. Learning Contract

  25. Learning Contract

  26. Learning Contract

  27. Learning Contract

  28. Objectives • Be able to calculate slope given 2 points. (cognitive) • Be able to recognize an when its appropriate to use an xy table. (cognitive) • After able to organize an xy table, be able to plot the appropriate points on a graph. (cognitive) • Be able to recognize what is slope and what is y intercept in slope intercept form. (cognitive) • Be able to apply slope and y intercept when graphing a line. (cognitive)

  29. Websites that were handy • http://www.drmath.com • http://www.purplemath.com • http://www.algebrahelp.com • http://www.webmath.com • http://www.mathworld.wolfram.com • http://www.hotmath.com - game • http://www.songsforteaching.com/index.html - song on slope intercept