1. Lesson 12-1 Inverse Variation

2. Objectives Graph inverse variations Solve problems involving inverse variations

3. Vocabulary xxxxx –

4. Four Step Problem Solving Plan Step 1: Explore the Problem –Identify what information is given (the facts) –Identify what you are asked to find (the question) Step 2: Plan the Solution –Find an equation the represents the problem –Let a variable represent what you are looking for Step 3: Solve the Problem –Plug into your equation and solve for the variable Step 4: Examine the Solution –Does your answer make sense? –Does it fit the facts in the problem?

5. Example 1 Manufacturing The owner of Superfast Computer Company has calculated that the time t in hours that it takes to build a particular model of computer varies inversely with the number of people p working on the computer. The equationcan be used to represent the people building a computer. Complete the table and draw a graph of the relation. p24681012 t Original equation Replace p with 2. Divide each side by 2. Simplify. Solve for

6. Example 1 cont p24681012 t 6 Solve the equation for the other values of p. 321.51.21 Answer: Graph the ordered pairs: (2, 6), (4, 3), (6, 2), (8, 1.5), (10, 1.2), and (12, 1). As the number of people p increases, the time t it takes to build a computer decreases.

7. Example 2 Inverse variation equation The constant of variation is 4. Graph an inverse variation in which y varies inversely as x and Solve for k. xy –4–1 –2 –1–4 0 undefined 14 22 41 Choose values for x and y whose product is 4.

8. Example 3 Method 1Use the product rule. Product rule for inverse variations Divide each side by 15. Simplify. If y varies inversely as x and find x when

9. Example 3 cont Method 2Use a proportion. Proportion rule for inverse variations Cross multiply. Divide each side by 15. Answer:Both methods show that

10. Example 4 If y varies inversely as x and find y when Use the product rule. Product rule for inverse variations Divide each side by 4. Simplify. Answer:

11. Example 5 Physical Science When two objects are balanced on a lever, their distances from the fulcrum are inversely proportional to their weights. How far should a 2-kilogram weight be from the fulcrum if a 6-kilogram weight is 3.2 meters from the fulcrum?

12. Example 5 cont Original equation Divide each side by 2. Simplify. Answer:The 2-kilogram weight should be 9.6 meters from the fulcrum.

13. Summary & Homework Summary: –The product rule for inverse variations states that if (x 1, y 1 ) and (x 2, y 2 ) are solutions of an inverse variation, then x 1 y 1 = k and x 2 y 2 = k –You can use proportions to solve problems involving inverse variations Homework: –pg x 1 y 2 ---- = ----- x 2 y 1