3 1 ACED A 2 Create equations in

3 -1 A-CED. A. 2 Create equations in two or more variables to represent Lines and Angles relationships between quantities; graph equations on coordinate axes with labels and scales. A-CED. A. 4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Ø Combined variation Ø Inverse variation Ø Joint variation Holt Geometry

3 -1 Lines and Angles { Paper for notes { Pearson 8. 1 { Graphing Calc. Holt Geometry

TOPIC: 3 -1 Lines Name: Daisy Basset and Angles Period: 8. 1 Inverse Variation Objective: Date : Subject: Notes Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Holt Geometry

3 -1 Lines and Angles Vocabulary Ø Direct Variation Ø Inverse Variation Holt Geometry

3 -1 Lines and Angles 1. Is the relationship between the variables a direct variation, an inverse variation, or neither? Write function models for the direct and inverse variations. Holt Geometry

3 -1 Lines and Angles A. x 2 4 10 15 y 15 7. 5 3 2 xy 30 30 As x increases , y decreases. It may vary inversely. Test to see whether xy is constant. y varies inversely to x. The function is Holt Geometry .

3 -1 Lines and Angles B. x 2 4 10 15 As x increases , y decreases. xy 20 It may vary inversely. y 10 8 32 3 30 Test to see whether 1. 5 22. 5 xy is constant. Since the products are not constant, the relationship is neither. Holt Geometry

3 -1 Lines and Angles C. x y 0. 2 0. 5 1 1. 5 8 20 40 60 As x increases , y increases. 40 It may vary directly. 40 Test to see whether is constant. 40 y varies directly to x. The function is Holt Geometry .

3 -1 Lines and Angles 2. Holt Geometry Suppose x and y vary inversely, and x = 4 when y = 12.

3 -1 Lines and Angles A. What function models the inverse variation. Holt Geometry

3 -1 Lines and Angles The function is Holt Geometry .

3 -1 Lines and Angles B. What is y when x = 10? y = 4. 8 when x = 10. Holt Geometry

3 -1 Lines and Angles { Notes 8. 1 day 2 { Calculator Holt Geometry

C. Suppose x and y vary inversely, and x = 8 when y = -7. What is the function that models the inverse variation? 3 -1 Lines and Angles Holt Geometry

3 -1 Lines and Angles The function is Holt Geometry .

3 -1 Lines and Angles 3. Each pair of values is from a direct variation. Find the missing value. Holt Geometry

3 -1 Lines and Angles (x, 12)(4, 1. 5) y = kx 1. 5 = k 4 Holt Geometry

3 -1 Lines and Angles (x, 12) y = kx 12 = 0. 375 x x = 32 Holt Geometry

4. Each pair of values is from a inverse variation. Find the missing value. 3 -1 Lines and Angles Holt Geometry

3 -1 Lines and Angles (x, 12)(4, 1. 5) Holt Geometry

(x, 12) 3 -1 Lines and Angles Holt Geometry

3 -1 Lines and Angles Holt Geometry

3 -1 Lines and Angles { Notes 8. 1 { Calculator Holt Geometry

3 -1 Lines and Angles 5. Your math class has decided to pick up litter each weekend in a local park. Each week there is approximately the same amount of litter. Holt Geometry

3 -1 Lines and Angles The table shows the number of students who worked each of the first four weeks of the project and the time needed for the pickup. Holt Geometry

3 -1 Lines and Angles A. # of students (n) Time in minutes (t) 3 5 12 17 85 51 21 15 nt 255 252 255 less The more students who help, the ___ time the cleanup takes. It may vary inversely. Test to see whether nt is constant. Holt Geometry

nt is almost always 255. In real life data, 252 is close enough. Inverse variation is still a good model. 3 -1 Lines and Angles The function is Holt Geometry .

3 -1 Lines and Angles B. How many students should there be to complete the project in at most 30 minutes each week? Holt Geometry

3 -1 Lines and Angles 30 n = 255 n = 8. 5 9 There should be at least __ students to do the job in at most 30 minutes. Holt Geometry

3 -1 Lines and Angles Summary D L I Q Holt Geometry Summarize/reflect What did I do? What did I learn? What did I find most interesting? What questions do I still have? What do I need clarified?

3 -1 Lines and Angles Hmwk 8. 1 C Math XL Start Notes 8. 2 Work on the Study Plan Holt Geometry

3 -1 8. 2 The Reciprocal Function Family TOPIC: Lines and Name: Angles Daisy Basset Period: Objective: Date : Subject: Notes Identify the effect on the graph of replacing f(x) by f(x) + k and f(x+h) for specific values of h and k (both positive and negative). Holt Geometry

3 -1 Lines and Angles Key Concepts Ø General Form of the Reciprocal Function Family Ø The Reciprocal Function Family Holt Geometry