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8.1-Variation Models

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- 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”

- 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

- 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.

- 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

- 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: 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

- 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

- 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