8.1-Variation Models

1. 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”

2. 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

3. 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.

4. 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

5. 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.

6. 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

7. 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

8. 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