3.15 Notes A2
- 2. Section 3.15: Two basic graphs: y = cx & y = c x y = cx Describes the relationship between things that are in a constant ratio. ( ) Ex. 1: The days in each week. Ex. 2: The weeks in each year. Ex. 3: The minutes in each hour. Your turn: 1. Write a direct variation equation to represent the number of hours in a day. 2. Write a direct variation equation to represent the number of feet in an inch. 2
- 3. Using these Use the information and the corresponding equation equations: to find the requested value. 1. If 120 hours have past since your birthday, how many days is that? 2. If a cabinet in your house is 4 feet 6 inches tall, how many inches is that? 3. If you have been working at your job for 37 weeks, how many years is that? Thinking about When your situation is modeled by direct variation, what these if: equations mean: 1. One quantity doubles, then: 2. One quantity decreases, then: 3. One quantity stays the same, then: 3
- 4. What do these Let's say that for each cookie I eat, my sister eats equations look three times as many. What is the equation like as graphs? representing this situation? Now, let's graph the equation to investigate the solutions. x y What do you notice about this graph? 4
- 5. Your Turn: Each time a student babysits, they make $30. Write a direct variation equation and graph it. x y 5
- 6. y = c Describes the relationship between things that have a constant product. x Ex. 1: Suppose you have $100 to divide equally ( ) among your friends. What are some ways you could do this? Ex. 2: A rectangle has an area of 80 in2. What are the possibilities for the length and width? 6
- 7. Let's look at the Some of the values we came up with for length rectangle and width are: example from before. Let's graph these and see what happens... What about the places between these points? Would these in between points also make the rectangle's area 800? Is there an equation for this graph? 7
- 8. Another Inverse What does the graph of inverse variation look like Variation Equation: in general? Ex. 1: xy = 10 x y What can x not equal in these equation??? Why? Ex. 2: xy = ‐6 x y Why do these equations have two branches, but the rectangle problem only had one branch? 8
- 9. Homework: p. 281 #1, 2, 3abc, 4abc, 5, 7bc, 10, 12, 14 9
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