Direct Variation & Inverse Variation (SOL A.8)

1. Direct Variation & Inverse Variation (SOL A.8) Chapters 5-2 & 11-6

2. Direct Variation • If the ratio between two variables is a constant, than a direct variation exists. • A direct variation can be written in the form of y = kx, where k is the constant of variation.

3. Inverse Variation • Is the product of two variables is a constant, then an inverse variation exists. • An inverse variation can be written in the form y = k/x or xy = k.

4. Examples of Direct Variations • 7y = 2x • 3y + 4x = 8

5. Your Turn • Does the following represent a direct variation? If so, find the constant of variation. • 4x + 5y = 0

6. Writing an equation for a direct variation • First thing----find the constant of variation kusing, an ordered pair, other than (0, 0), that you know is a solution of the equation. • Look at Problem 2 on page 300 in your textbook.

7. Graphing a Direct Variation • Problem 3 on page 300

8. Graphs of Direct Variations

9. Writing a Direct Variation from a Table

10. Moving on to Inverse Variation • An equation of the form xy = k or y = k/x, where k ≠ 0, is an inverse variation. • The constant of variataion for an inverse variation is k, the product x ∙ y for an ordered pair (x, y) that satisfies the inverse variation.

11. Writing an Equation Given a Point • Problem 1 on page 686

12. Using Inverse Variation • Problem 2 page 687

13. Examples of Graphs of Inverse Variations

14. Graphing an Inverse Variation • Pg 688 Problem 3

15. Comparing Direct & Inverse Variations

16. Determining Direct or Inverse Variation

17. Identifying Direct or Inverse Variation • Page 689 Problem 5