1 / 20

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:

Download Presentation

Direct Variation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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.

More Related