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Objectives

5.3/11.1 Direct and Indirect Variation. Objectives. Solve and graph direct- and indirect variation equations. NCSCOS. 1.02, 1.03, 3.03, and 4.01. 5.3/11.1 Direct and Indirect Variation. Direct Variation (Lesson 5-3). y x.

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Objectives

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  1. 5.3/11.1 Direct and Indirect Variation Objectives • Solve and graph direct- and indirect variation equations. NCSCOS 1.02, 1.03, 3.03, and 4.01

  2. 5.3/11.1 Direct and Indirect Variation Direct Variation (Lesson 5-3) yx If y varies directly as x, then y = kx , where k is the constant of variation = k (if you divide y by x in the table, you will find ‘k’) k = -3 y = -3x direct variation equation:

  3. = k ; = k ; = k ; 28 -26 15 -5 2 -2 5.3/11.1 Direct and Indirect Variation If y varies directly as x, and y = 15 when x = -5, find k, and write an equation of direct variation. y = -3x k = -3 If y varies directly as x, and y = 28 when x = 2, find k, and write an equation of direct variation. y = 14x k = 14 If y varies directly as x, and y = -26 when x = -2, find k, and write an equation of direct variation. y = 13x k = 13

  4. = k ; = k ; = k ; -7.5 -7 15 1.5 -6 -14 5.3/11.1 Direct and Indirect Variation If y varies directly as x, and y = -7.5 when x = 1.5, find k, and write an equation of direct variation. y = -5x k = -5 If y varies directly as x, and y = -7 when x = -14, find k, and write an equation of direct variation. 1 1 y = x k = 2 2 If y varies directly as x, and y = 15 when x = -6, find k, and write an equation of direct variation. 5 5 y = –x k = – 2 2

  5. = = = 8 27 36 6 9 4 5.3/11.1 Direct and Indirect Variation If y varies directly as x, and y = 27 when x = 6, find x, when y = 45. 45 x = 10 x If y varies directly as x, and y = 8 when x = 4, find x, when y = 160. 160 x = 80 x If y varies directly as x, and y = 36 when x = 9, find x, when y = 48. 48 x = 12 x

  6. = = = -119 35 126 9 7 7 5.3/11.1 Direct and Indirect Variation If y varies directly as x, and y = 35 when x = 7, find y, when x = 84. y y = 420 84 If y varies directly as x, and y = -119 when x = 7, find x, when y = -51 -51 x = 3 x If y varies directly as x, and y = 126 when x = 9, find y, when x = 3 y y = 42 3

  7. 5.3/11.1 Direct and Indirect Variation Indirect Variation (Lesson 11-1) If y varies indirectly or inversely or as x, then, k x k 0, and x 0 and xy = k y = (if you multiply y & x in the table, you will find ‘k’) k = 60 60 y = inverse variation is x

  8. k k 5 = -10 = 24 -2 5.3/11.1 Direct and Indirect Variation Solve for k and the inverse equation. If y varies inversely as x and y = 5 when x = 24. k = 120 120 y = x If y varies inversely as x and y = -10 when x = -2 20 y = k = 20 x If y varies inversely as x and y = 3 when x = 8 k 24 k = 24 3 = y = 8 x

  9. k k 7 = 8 = -17 3 5.3/11.1 Direct and Indirect Variation If y varies inversely as x and y = 7 when x = 3 21 y = k = 21 x If y varies inversely as x and y = -7 when x = -10 k 70 k = 70 y = -7 = -10 x If y varies inversely as x and y = 8 when x = -17 -136 k = -136 y = x

  10. 5.3/11.1 Direct and Indirect Variation If y varies inversely as x and y = 7 when x = 13 find y when x = 10 y = 9.1 (7)(13) = 10y If y varies inversely as x and y = 7 when x = 13 find x when y = 3.5 (7)(13) = 3.5x x = 26 If y varies inversely as x and y = -2 when x = 9 find y when x = -3 (-2)(9) = -3y y = 6 If y varies inversely as x and y = -2 when x = 9 find x when y = 7.2 (-2)(9) = 7.2x x = -2.5

  11. 5.3/11.1 Direct and Indirect Variation If y varies inversely as x and y = 6 when x = 11 find y when x = 2.5 y = 26.4 (6)(11) = 2.5y If y varies inversely as x and y = 6 when x = 11 find x when y = 8 (6)(11) = 8x x = 8.25 If y varies inversely as x and y = 3 when x = 16 find y when x = 6.4 (3)(16) = 6.4y y = 7.5 If y varies inversely as x and y = 3 when x = 16 find x when y = 10.667 (3)(16) = 7.5x x = 4.5

  12. 5.3/11.1 Direct and Indirect Variation The area of a rectangle is 36 square centimeters. What is the length of a rectangle with the same area and a width of 3 centimeters? area = 36 cm2; width = 3 cm length = 12 cm The area of a triangle is constant, the length of the base varies inversely as the height. When the base is 22 centimeters, the height is 36 centimeters. What should the length of the base be when the height is 24 centimeters in order to maintain a constant area? area = 396 cm2; height = 24 cm base = 33 cm

  13. 5.3/11.1 Direct and Indirect Variation The speed at which a gear revolves varies inversely as the number of teeth on a gear. If a gear with 16 teeth revolves at a speed of 500 revolutions per minute, at what speed should a gear with 20 teeth revolve? 400 rpm The pitch of a musical note varies inversely as its wavelength. If the tone has a pitch of 440 vibrations per second and a wavelength of 2.4 feet, find the pitch of a tone that has a wavelength of 1.6 ft. 660 vibrations per second

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