Understanding Direct Variations in Mathematics

1. Grade Distribution Reassessments and Make-ups due Thursday, Feb 5th 4.6: Direct Variations 10/19/2012 8:16 AM 10/19/2012 8:16 AM 1 1

2. Direct and Inverse Variations Section 8-1 4.6: Direct Variations

3. Direct Variation A. Direct Variation:A linear function which two variables are which one is a constant multiple of the other; when one variable changes the other changes in proportion to the first y x 4.6: Direct Variations

4. Direct Variation B. Direct Variation: • K = Constant of Variation or SLOPE • There is NO y-intercept • X= Independent Variable • Y = Dependent Variable • If X goes up, Y has to go up. • If X goes down, Y has to go down. C. KEYWORD: VARY(ies) DIRECTLY or DIRECTLY PROPORTIONAL • Divide the variables • Yvaries directly with X • k is not always going to be used in all questions • It is used only when the problem is comparing itself 4.6: Direct Variations

5. Example 1 Tell whether the equation, 2x – 3y = 0 represents direct variation. Identify the constant of variation. 4.6: Direct Variations

6. Example 2 Tell whether the equation, 2x + y = 3 represents direct variation. Identify the constant of variation. 4.6: Direct Variations

7. Your Turn Tell whether the equation, 3x + 8y = 0 represents direct variation. Identify the constant of variation. 4.6: Direct Variations

8. Example 3 The weekly salary a woman earns, S, varies directly as the number of hours, h, which she works.  Express this relation as a formula. 4.6: Direct Variations

9. Example 4 The resistance R, of a copper wire, varies directly as its length L.  Write this relation as a formula using k as the constant of variation. 4.6: Direct Variations

10. Your Turn At a recycling center, computers and computer accessories can be recycled for a fee f based on weight, w.  Write this relation as a formula using k as the constant of variation. 4.6: Direct Variations

11. Example 5 Would this situation be a direct variation? Your weekly pay, p, is directly proportional to the number of hours, h, she works at the record store. 4.6: Direct Variations

12. Example 6 Would this situation be a direct variation? If the area (A) of a rectangle remains constant and the width (w) decreases. 4.6: Direct Variations

13. Your Turn Would this situation be a direct variation? If the temperature is constant, the pressure of a gas (P) in a container varies inversely as the volume of the container (V). 4.6: Direct Variations

14. Example 7 If a varies directly as b and a = 3 when b = 24, find b when a = 10. • Would k be necessary into this equation? • Another way of finding out this problem is through proportions. 4.6: Direct Variations

15. Example 8 If yvaries directly with x. If y = 4 when x = 2, find y when x = –6. 4.6: Direct Variations

16. Example 9 If y varies directly as x2and y = 64 when x = 2, find y when x = 8. 4.6: Direct Variations

17. Your Turn If yvaries directly with x. If y = 75 when x =25, find x when y = 25. 4.6: Direct Variations

18. Assignment Worksheet 4.6: Direct Variations

19. Example 3 The values of y and x vary directly. Determine the constant variation if x = 3 when y = 12. 4.6: Direct Variations 10/19/2012 8:16 AM 8-1: Direct and Inverse Variations 19

20. 4.6: Direct Variations