Reassessments and Make-ups Grade Distribution 3rd 6th 7th A 3 2 B 9 13 10 C 7 6 D 5 F No Show 4 Avg. 81.25 78.93 79.95 Reassessments and Make-ups due Thursday, Feb 5th 12/1/2018 2:31 AM 4.6: Direct Variations 12/1/2018 2:31 AM 12/1/2018 2:31 AM 1 1

Direct and Inverse Variations Section 8-1 12/1/2018 2:31 AM 4.6: Direct Variations

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 12/1/2018 2:31 AM 4.6: Direct Variations

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 Y varies directly with X k is not always going to be used in all questions It is used only when the problem is comparing itself 12/1/2018 2:31 AM 4.6: Direct Variations

Example 1 Tell whether the equation, 2x – 3y = 0 represents direct variation. Identify the constant of variation. 12/1/2018 2:31 AM 4.6: Direct Variations

Example 2 Tell whether the equation, 2x + y = 3 represents direct variation. Identify the constant of variation. 12/1/2018 2:31 AM 4.6: Direct Variations

Your Turn Tell whether the equation, 3x + 8y = 0 represents direct variation. Identify the constant of variation. 12/1/2018 2:31 AM 4.6: Direct Variations

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. 12/1/2018 2:31 AM 4.6: Direct Variations

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. 12/1/2018 2:31 AM 4.6: Direct Variations

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. 12/1/2018 2:31 AM 4.6: Direct Variations

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. 12/1/2018 2:31 AM 4.6: Direct Variations

Example 6 Would this situation be a direct variation? If the area (A) of a rectangle remains constant and the width (w) decreases. 12/1/2018 2:31 AM 4.6: Direct Variations

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). 12/1/2018 2:31 AM 4.6: Direct Variations

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. 12/1/2018 2:31 AM 4.6: Direct Variations

Example 8 If y varies directly with x. If y = 4 when x = 2, find y when x = –6. 12/1/2018 2:31 AM 4.6: Direct Variations

Example 9 If y varies directly as x2 and y = 64 when x = 2, find y when x = 8. 12/1/2018 2:31 AM 4.6: Direct Variations

Your Turn If y varies directly with x. If y = 75 when x =25, find x when y = 25. 12/1/2018 2:31 AM 4.6: Direct Variations

Assignment Worksheet 12/1/2018 2:31 AM 4.6: Direct Variations

8-1: Direct and Inverse Variations Example 3 The values of y and x vary directly. Determine the constant variation if x = 3 when y = 12. 12/1/2018 2:31 AM 4.6: Direct Variations 12/1/2018 2:31 AM 8-1: Direct and Inverse Variations 19

12/1/2018 2:31 AM 4.6: Direct Variations