Algebra 2 Notes May 19, 2009

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

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

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 xy xy

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

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.

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 __________

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