1. Insert Lesson Title Here Course 2 Identifying IV QUESTION What are the three ways to show inverse variation?

2. 3 ways to show inverse variations: Insert Lesson Title Here Course 2 Identifying IV * by a table * by an equation * by a graph

3. Insert Lesson Title Here Course 2 Identifying IV QUESTION How can a table show inverse variation?

4. Table Insert Lesson Title Here Course 2 Identifying IV - either x increases and y decreases, or x decreases and y increases (vary inversely) - the product of each x and corresponding y is the same x30155 y126

5. Example of Indirect Variation: 1. As x increases (3, 12, 48), y decreases 8, 2, 1/3). 2. What is the constant of variation of the table above? 3 8 = k or k = 24 12 2 = k or k = 24 48 1/3 = k or k =24Note k stays constant. xy 38 481/3 122 Course 2 Identifying IV

6. Do these tables show IV? Insert Lesson Title Here Course 2 Identifying IV x1½¼ y4816 x-202 y10 x4.530.5 y2318 x-24-12-8 y-½-1 ½ YES NOYES

7. Insert Lesson Title Here Course 2 Identifying IV QUESTION How can an equation show inverse variation?

8. Equation Insert Lesson Title Here Course 2 Identifying IV - written in the form: y = k/x - other possible form: xy = k - k = 0 Example: y = 4/x

9. Do these equations show IV? Insert Lesson Title Here Course 2 Identifying IV y = 6x 2y = x y/8 = 1/x y = 3.4/x NO YES xy = -12 YES y = -4/x + 2 NO

10. Insert Lesson Title Here Course 2 Identifying IV QUESTION How can a graph show inverse variation?

11. Graph Insert Lesson Title Here Course 2 Identifying IV - curved line formed by connected points will NOT go through the origin - approaches the axes but never crosses them

12. Do these graphs show IV? Insert Lesson Title Here Course 2 Identifying IV NO YES NO YES

13. Insert Lesson Title Here Course 2 Identifying IV QUESTION What is the proportion for indirect or inverse variation?

14. Proportion: Insert Lesson Title Here Course 2 Identifying IV 1. Arrange one pair as the numerator of one ratio and the denominator of the other. 2. Arrange the other pair in the same manner.

15. Insert Lesson Title Here Course 2 Identifying IV VOCABULARYKIM inverse variation - one variable increases, other decreases - product of variables x and y is constant y = k/x

16. Is this an inverse variation? Course 2 Identifying IV