1. Algebra 2 Notes May 19, 2009

2. Warm-Ups Remembering Direct Variation If you need help remembering, refer to page 74 Example 4 y varies directly with x: a) Given that x = 2 when y = 4, find y when x = 5 b) Given that x = 1 when y = 5, find y when x = 3 c) Given that x = 10 when y = 3, find y when x = 4

3. Direct Variation vs. Indirect Variation Direct Variation: x and y vary directly with each other When one variable increases, the other increases as well When one variable decreases, the other decreases as well Indirect Variation: x and y vary inversely with each other When one variable increases, the other decreases

4. Direct Variation vs. Indirect Variation If it is direct variation, x divided by y will be the same for all values If it is inverse variation x times y will be the same for all values Are the following examples inverse variation, direct variation, or neither? xy 0.51.5 26 618 xy 0.212 0.64 1.22 xy 12 21 30.5

5. Writing an Equation Ex 1) Suppose that x and y vary inversely, and x = 3 when y = -5. Write the function that models the inverse variation. (First find the value for k, then plug that into ) Ex 2) Suppose that x and y vary inversely, and x = 0.3 when y = 1.4. write the function that models the inverse variation

6. Joint Variation Page 490 Combined VariationEquation Form z varies jointly with x and y z varies jointly with x and y and inversely with w. z varies directly with x and inversely with wy.

7. Real World Connection Physics: Newton’s Law of Universal Gravitation is modeled by the following formula: F is the gravitational force between two objects with masses m 1 and m 2, and d is the distance between the two objects. G is the gravitational constant. Describe Newton’s law as a combined variation: F varies jointly with __________ F varies inversely with __________

8. Homework #63 Page 491 #1, 4, 7, 8, 12, 13, 17, 18, 23, 24, 27, 60-62