8 1 variation models
This presentation is the property of its rightful owner.
Sponsored Links
1 / 8

8.1-Variation Models PowerPoint PPT Presentation


  • 43 Views
  • Uploaded on
  • Presentation posted in: General

8.1-Variation Models. a is the constant of variation Direct Variation As x ↑, y ↑ ( Multiplication if y alone) “y varies directly with x” Inverse (indirect) Variation As x ↑, y ↓ ( Division if y alone: ) “y varies inversely with x”. Examples:.

Download Presentation

8.1-Variation Models

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


8 1 variation models

8.1-Variation Models

  • a is the constant of variation

  • Direct Variation

    As x ↑, y ↑

    (Multiplication if y alone)

    “y varies directly with x”

  • Inverse (indirect) Variation

    As x ↑, y ↓

    (Division if y alone: )

    “y varies inversely with x”


Examples

Examples:

  • 1. Are the following direct, inverse or neither?

    A) xy=7

    B) y = x + 3

    C)

    D) y=2x

    E) y=

    F) 3x=y

    G) xy=0.75

    H) y=2x-5

    2. Text # 21 & 23


Examples1

Examples:

  • 3. y varies inversely with x, and y=7 when x=4. Write an equation that relates x and y. Then find y when x=-2.


Examples2

Examples:

  • X and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=2.

  • 4. x=4, y=3

  • 5. x=8, y=-1

  • 6. x= ½, y=12


Examples3

Examples:

  • 7. y varies directly with x, and x=2 when y=8. Write an equation relating x and y. Then find y when x=5.

  • 8. x and y vary directly and x=-2 when y=12. Write and equation relating x and y. Then find y when x=1/2.


Joint variation

Joint Variation

  • Joint Variation: When a quantity varies directly with the PRODUCT of TWO OR MORE quantities. (a is the constant of variation)

  • Ex: z=axy z varies jointly with x and y

  • Ex: p=aqrs p varies jointly with q, rand s


Examples4

Examples:

  • 9. Write the equations relating x, y and z given that z varies jointly with x and y. Then find z when x=-2 and y=5.

  • A) x=1, y=2, z=7

  • B) x=4, y=-3, z=24

  • C) x=-6, y=-4, z=56


Examples5

Examples:

  • 10. Write an equation for the relationship.

  • A) x varies inversely with y and directly with w

  • B) p varies jointly with q and r and inversely with s.

  • C)f varies jointly with m and the square of b


  • Login