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Inverse Variations

Inverse Variations . Lesson 11-6. An equation in the form of ____________________ or ____________ is an inverse variation,. The constant of variation is _______, the _______________ of x and y for an ordered pair (x, y) that solves the inverse variation. xy =k. k. product.

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Inverse Variations

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  1. Inverse Variations Lesson 11-6

  2. An equation in the form of ____________________ or ____________ is an inverse variation,. The constant of variation is _______, the _______________ of xand y for an ordered pair (x, y) that solves the inverse variation. xy =k k product Writing an Equation For an Inverse Variation, given a Point A. Suppose y varies inversely with x, and y = 8, when x = 3. What is an equation for the inverse variation? _______________ (the general form of an inverse variation) _______________ (Substitute known values) _______________ (simplify) _______________ (Write the equation.) xy =k (3)(8) =k 24=k xy = 24 or

  3. Suppose y varies inversely with x, and y = 9 when x = 6. What is an equation for the inverse variation? _______________ (the general form of an inverse variation) _______________ (Substitute known values) _______________ (simplify) _______________ (Write the equation.) xy =k (6)(9) =k 54=k xy = 54 or

  4. USING INVERSE VARIATION: The weight needed to balance a lever varies inversely with the distance from the fulcrum to the weight. How far away would a 160 pound person have to be to balance a 1000 pound elephant that is 7 feet away from the fulcrum? weight1 ● distance 1 = weight 2 ● distance 2 ________________________ = ________________ _______________ = ________________ _______________ = ________________ 1000(7) 160 d 160 d 7,000 d = 43.75 ft

  5. A 120-pound weight is placed on a lever, 5 feet from the fulcrum. How far away from the fulcrum should an 80-pound weight be placed to balance the lever? weight1 ● distance 1 = weight 2 ● distance 2 80(d) (120)(5) = 600 = 80d 7.5 ft. = d

  6. -1 -2 -4 -8 8 4 2 1 Und.

  7. Graph the equation xy = –8 y = ___________

  8. Graph must pass through origin (0,0) and is a straight line.

  9. The constant (k) is equal to the product of x and y (k=xy).

  10. Determining Direct or Inverse Variation To determine if a table or set of data is a direct variation, check each ratio . . If they are constant, then it is a direct variation with the equation y = kx or If it is not a direct variation, check the product of xy and see if that is constant. If it is, you have an inverse variation with the equation xy = k or Determine if the table represents a direct variation or an inverse variation. Write an equation for the table.   Since the ratio is constant (-5), this is a direct variation. The equation is y = 5x

  11. Check the ratio of y/x to see if it is a direct variation. Since 4.5 ≠ 1.125, this is not a direct variation. Check the product of xy to see if this is an inverse variation. (2)(9) = 18 (4)(4.5) = 18 (6)(3) = 18 Since the product of xy is constant, this is an inverse variation. The equation is xy = 18 or

  12. Direct or Inverse Variation: Real-World Examples • I. The cost of a $120 boat rental is split among several friends. • Does this represent an example of a direct variation or an • inverse variation? • J. You download several movies for $14.99 each. Is this an example • of a direct variation or an inverse variation? Write an equation to model the situation: Cost per person times the number of people = boat rental c ● n = 120 Since this is in the form of xy=k, this is an inverse variation. Write an equation to model the situation: Total cost = Cost per movie times the number of movies C = 14.99 ● n Since this is in the form of y = kx, this is a direct variation.

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