# 8.1-Variation Models - PowerPoint PPT Presentation

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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:.

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8.1-Variation Models

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### 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:

• 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

### 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.

### 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

### 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: 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

### 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

### 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