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Direct Variation

Direct Variation. What is it and how do I know when I see it?. Definition: y varies directly as x means that y = kx where k is the constant of variation. Another way of writing this is k =. In other words:

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Direct Variation

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  1. Direct Variation What is it and how do I know when I see it?

  2. Definition: y varies directly as x means that y = kx where k is the constant of variation. Another way of writing this is k = In other words: * the constant of variation (k) in a direct variation is the constant (unchanged) ratio of two variable quantities.

  3. Examples of Direct Variation: Note: x increases, 6 , 7 , 8 And y increases. 12, 14, 16 What is the constant of variation of the table above? Since y = kx we can say Therefore: 12/6=k or k = 2 14/7=k or k = 2 16/8=k or k =2 Note k stays constant. y = 2x is the equation!

  4. Examples of Direct Variation: Note: x decreases, 10, 5, 3 And y decreases. 30, 15, 9 What is the constant of variation of the table above? Since y = kx we can say Therefore: 30/10=k or k = 3 15/5=k or k = 3 9/3=k or k =3 Note k stays constant. y = 3x is the equation!

  5. Examples of Direct Variation: Note: x decreases 9, 4, 2 And y decreases. 45, 20, 10 What is the constant of variation of the table above? Since y = kx we can say Therefore: 45/9=k or k = 5 10/2=k or k = 5 50/4=k or k = 5 Note k stays constant. y = 5x is the equation!

  6. Answer Now What is the constant of variation for the following direct variation? • 4 • 2 • ½ • ¼

  7. What is the constant of variation for the following direct variation? 4 2 ½ ¼ Answer Now

  8. What is the constant of variation for the following direct variation? 3 2 1/3 ½ Answer Now

  9. What is the constant of variation for the following direct variation? 2 5 10 ½ Answer Now

  10. Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 12/4 or 3 Equation? y = 3x

  11. Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 4/12 or 1/3 Equation? y = 1/3x

  12. Is this a direct variation? If yes, give the constant of variation (k) and the equation. No! The k values are different!

  13. Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 2/12 or 1/6 Equation? y = 1/6 x

  14. Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 6/4 or 3/2 or 1.5 Equation? y = 1.5 x

  15. Is this a direct variation? If yes, give the constant of variation (k) and the equation. No! The k values are different!

  16. Answer Now Which is the equation that describes the following table of values? • y = 5x • y = 2x • y = ½ x • xy = 200

  17. Which is the equation that describes the following table of values? y = 1.5x y = 2x y = 2.5 x y = 20x Answer Now

  18. Which is the equation that describes the following table of values? y = 4x y = 2x y = ½x y = ¼x Answer Now

  19. Which is the equation that describes the following table of values? y = 6x y = 4x y = ½ x xy = 2x Answer Now

  20. Definition: y varies directly as x means that y = kx where k is the constant of variation. Another way of writing this is k = In other words: * the constant of variation (k) in a direct variation is the constant (unchanged) ratio of two variable quantities.

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