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Unit 3 Lesson 4 - TEXTBOOK 5.2 & 12.1 D IRECT AND INVERSE VARIATION

Unit 3 Lesson 4 - TEXTBOOK 5.2 & 12.1 D IRECT AND INVERSE VARIATION. Variation relates to 2 variables: like x and y or age and height. (same as the slope or the constant rate of change). ...so, DIRECT VARIATION is a special name for the lines that include

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Unit 3 Lesson 4 - TEXTBOOK 5.2 & 12.1 D IRECT AND INVERSE VARIATION

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  1. Unit 3 Lesson 4 - TEXTBOOK 5.2 & 12.1 DIRECT AND INVERSE VARIATION Variation relates to 2 variables: like x and y or age and height (same as the slope or the constant rate of change) ...so, DIRECT VARIATION is a special name for the lines that include ( 0 , 0 ) - the origin - in their solutions. This is because there is no # added or subtracted at the end of the equation. Examples: y = 5x y = -1/2x y = .05x

  2. Example 1 proves that the k is the same thing as slope and rate of change.

  3. Example 2 shows you that the origin is ALWAYS a solution (so always on the line!) It should be used with the slope to graph as shown below.

  4. QUICK PRACTICE on handout

  5. Finally, it gets a little more difficult! Example 4 walks through how you write and solve these types of equations... * Since the k or constant is the same as the Rate of Change or Slope, you can think of this as using the slope formula. (7, 28) and (0,0) so 28-0/7-0 = 4/1 For b. plug the value given into the equation you wrote.

  6. class example

  7. Try these... more class examples, or ticket out the door. 7. k = 4 so y = 4x and x = 8 8. k = 3 so y = 3x and x = 5 9. k = -2 so y = -2x and y = 12 10. k = -3 so y = -3x and y = 15 11. k = 4 so y = 4x and y = 24 12. k = 2/3 so y = 2/3x and x = -24

  8. HOMEWORK: PRACTICE WORKBOOK 5-2 # 1-9

  9. Direct Variation equations often occur outside Math class... Example: C = dπ d = rt

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