Understanding Inverse Variation in Algebra 2 Lesson 9-1

1. Ch. 9.1 Inverse Variation

2. k x y = x and y vary inversely. k 7 4 = Substitute the given values of x and y. 28 x y = Use the value of k to write the function. Inverse Variation ALGEBRA 2 LESSON 9-1 Suppose that x and y vary inversely, and x = 7 when y = 4. Write the function that models the inverse variation. 28 = kFind k. 9-1

3. Check understanding #1 p. 479

4. = / a. x –2 4 6 y 5 –10 –15 x –2 –1.3 7 y 6 5 –4 x 2 4 14 y 0.7 0.35 0.1 So xy = 1.4 and the function is y = . 1.4 x b. Not all the products of x and y are the same (–2 • 6 –1.3 • 5). c. Inverse Variation ALGEBRA 2 LESSON 9-1 Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? Write functions to model the direct and inverse variations. As x increases, y decreases. The product of each pair of x- and y-values is 1.4. y varies inversely with x and the constant of variation is 1.4. As x increases, y decreases, but this is not an inverse variation. This is neither a direct variation nor an inverse variation. As x increases, y decreases. Since each y-value is –2.5 times the corresponding x-value, y varies directly with x and the constant of variation is –2.5, and the function is y = –2.5x. 9-1

5. Check understanding #2 A – C p. 479

6. Homework Page 481, Exercises: 2 – 14 e, 24 - 27