Copyright © 2008 Pearson Education, Inc Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Solve direct variation problems. Solve inverse variation problems. 7.8 Variation Solve direct variation problems. Solve inverse variation problems. 1 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Solve direct variation problems. Objective 1 Solve direct variation problems. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.8 - 3

Solve direct variation problems. Two variables vary directly if one is a constant multiple of the other. With direct variation, y varies directly as x if there exists a constant k such that 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. 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. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.8 - 4

Solve direct variation problems. (cont’d) 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. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.8 - 5

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

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

EXAMPLE 2 Solving a Direct Variation Problem 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. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.8 - 8

Solve inverse variation problems. Objective 2 Solve inverse variation problems. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.8 - 9

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. 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 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.8 - 10

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

EXAMPLE 4 Using Inverse Variation 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: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.8 - 12