1. Chapter 7 Section 8

2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Variation Solve direct variation problems. Solve inverse variation problems. 7.8 2

3. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Solve direct variation problems. Slide 7.8-3

4. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Two variables vary directly if one is a constant multiple of the other. Solve direct variation problems. In these equations, y is said to be proportional to x. The constant k in the equation for direct variation is a numerical value. This value is called the constant of variation. Direct Variation y varies directly as x if there exists a constant k such that Some simple examples of variation include: Direct Variation: The harder one pushes on a car’s gas pedal, the faster the car goes. Inverse Variation: The harder one pushes on a car’s brake pedal, the slower the car goes. Slide 7.8-4

5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving a Variation Problem Step 1: Write the variation equation. Step 2: Substitute the appropriate given values and solve for k. Step 3: Rewrite the variation equation with the value of k from Step 2. Step 4: Substitute the remaining values, solve for the unknown, and find the required answer. Slide 7.8-5 Solve direct variation problems. (cont’d)

6. Copyright © 2012, 2008, 2004 Pearson Education, Inc. If z varies directly as t, and z = 11 when t = 4, find z when t = 32. Solution: Slide 7.8-6 EXAMPLE 1 Using Direct Variation

7. Copyright © 2012, 2008, 2004 Pearson Education, Inc. The direct variation equation y = kx is a linear equation. Other kinds of variation involve other types of equations. Direct Variation as a Power y varies directly as the nth power of x if there exists a real number k such that Slide 7.8-7 Solve direct variation problems. (cont’d)

8. Copyright © 2012, 2008, 2004 Pearson Education, Inc. The circumference of a circle varies directly as the radius. A circle with a radius of 7 cm has a circumference of 43.96 cm. Find the circumference if the radius is 11 cm. Solution: Thus, the circumference of the circle is 69.08 cm if the radius equals 11 cm. Slide 7.8-8 EXAMPLE 2 Solving a Direct Variation Problem

9. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Solve inverse variation problems. Slide 7.8-9

10. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve inverse variation problems Unlike direct variation, where k > 0 and k increases as y increases. Inverse variation is the opposite. As one variable increases, the other variable decreases. Inverse Variation y varies inversely as x if there exists a real number k such that Also, y varies inversely as the nth power of x if there exists a real number k such that Slide 7.8-10

11. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Suppose y varies inversely as the square of x. If y = 5 when x = 2, find y when x = 10. Slide 7.8-11 EXAMPLE 3 Using Inverse Variation

12. Copyright © 2012, 2008, 2004 Pearson Education, Inc. If the cost of producing pairs of rubber gloves varies inversely as the number of pairs produced, and 5000 pairs can be produced for $0.50 per pair, how much will it cost per pair to produce 10,000 pairs? Solution: Slide 7.8-12 EXAMPLE 4 Using Inverse Variation

13. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Hl# 7.8 Book: Beginning Algebra Page 480 Exercises 20,21,22,24,26,28,30,32,33,34