Ch. 9.1 Inverse Variation

y = x and y vary inversely. 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. y = x and y vary inversely. k x 4 = Substitute the given values of x and y. k 7 28 = k Find k. y = Use the value of k to write the function. 28 x 9-1

Check understanding #1 p. 479

The product of each pair of x- and y-values is 1.4. 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. x 2 4 14 y 0.7 0.35 0.1 a. The product of each pair of x- and y-values is 1.4. As x increases, y decreases. y varies inversely with x and the constant of variation is 1.4. So xy = 1.4 and the function is y = . 1.4 x x –2 –1.3 7 y 6 5 –4 b. As x increases, y decreases, but this is not an inverse variation. Not all the products of x and y are the same (–2 • 6 –1.3 • 5). = / This is neither a direct variation nor an inverse variation. x –2 4 6 y 5 –10 –15 c. 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

Check understanding #2 A – C p. 479

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