Direct and Inverse Variation - PowerPoint

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					  Direct and Inverse Variation


Take notes when you see
this animated pencil.


           Take
           Notes
             Objectives

• Understand the specialized
  vocabulary
• Know the basic algebraic equations
  that represent direct and inverse
  variation
• Apply techniques for classifying the
  types of variation
         Direct Proportion
           Direct Variation
        Directly Proportional
• A relationship between two variables in
  which one is a “constant multiple” of the
  other. When one variable changes the
  “other changes in proportion” to the first.
• If y is directly proportional to x, the
  equation is of the form y = kx (where k is a
  constant).
    Example of Direct Variation
• Equation: y = 3x         x        y     y/x
• Variable y is directly   0   3   0
  proportional to x.
                           1        3    3/1=3
• Tripling x causes y to
  triple.                  2   3   6    6/2=3
                           3        9    9/3=3
                           4        12   12/4=3
                           5        15   15/5=3
Graph of Direct Variation
      y = 3x
               y




                            x
          Inverse Variation
         Inverse Proportion
       Inversely Proportional
• A relationship where the “product of two
  variables is a constant”. When one
  variable increases the other decreases in
  proportion so that the “product is
  unchanged”.
• If y is inversely proportional to x, the
  equation is of the form y = k/x (where k is
  a constant).
  Example of Inverse Variation
• Equation: y = 48/x           x   y        xy
• Variable y is inversely      1   48       48
  proportional to x.
                          3   2   24    1/3 48
• Tripling x causes y to
  one third. The product       3   16       48
  of x and y is always
  48.                          4   12       48
                               6   8        48
                               8   6        48
Graph of Inverse Variation
  y

  20

  18                                                     y = 48/x
  16

  14

  12

  10

  8

  6

  4

  2

  0
       0   2   4   6   8   10   12   14   16   18   20   x
        Do the following Qs
1. If all the HKIS items in the Dragon Shop
   are on sale for 85%, what will be the new
   cost for the following:
   a) a T-shirt that costs $70 originally
   b) a windbreaker jacket that cost $130
         originally
        Do the following Qs
2. If the scale on a map reads
   0.25 in. : 4 mi, calculate the following:
   a) find the actual distance from
        Metropolis to Smallville which has a
        measured map distance of 9.25 in.
   b) find the map distance from Smallville
        to Roswell which has an actual
        distance of 268 mi.
         Do the following Qs
3. If model yachts are built to 1 in / 9 ft of
   the actual size, calculate the following:
   a) find the model length of a Blue Tooth
       yacht which is 120 ft long.
   b) find the actual length of a K2 yacht
       which has a model length of 9.5 in.
        Do the following Qs
4. Circle the correct terminology to make
   true statements.
   a) Knowing that the distance is equal to
       speed times time (d = st), in a 100
       meters sprint, any speed is directly
       or inversely proportional to time?
   b) If the speed is constant, then any
       distance is directly or inversely
       proportional to time?
        Do the following Qs
5. Given that length and width are inversely
   proportional to a constant area of 90 m2,
   calculate the following:
   a) If the length is 15 m, what is the
        width?
   b) If you want to create a box with an
       area of 90 m2 that wraps around the
       Earth’s equator, you require a width
       of 38 million meters. What is the
       length of the box?
        Do the following Qs
6. Given that pressure (P) and volume (V)
   are inversely proportional to each other
   when temperature is constant, use
   P1V1 = P2V2 to calculate the following.
   a) If P1 = 1 atm and V1 = 4.5 Liters,
        find P2, if V2 = 1.5 L?
   b) If P1 = 0.5 atm and V1 = 4.5 Liters,
        find V2, if P2 = 1.0 atm?
        Do the following Qs
7. Circle the correct terminology to make
   true statements.
   In science, power (P) is defined by the
   work (W) done in a certain amount of
   time. P = W/t.
   a) If the work done is constant, then
       pressure is directly or inversely
       proportional to time?
   b) If the power is constant, then any
       work done is directly or inversely
       proportional to time?
         Do the following Qs
8. In order to have objects balanced on a
   double pan scale, the massleft times the
   distanceleft must equal to massright times
   the distanceright (mldl = mrdr).
                                    50 g
       20 g

               15 cm           Distance ?


   Calculate the distance needed away
   from the fulcrum (pivot) so that the 50g
   object will balance the left hand side.
         Do the following Qs
9. In order to have objects balanced on a
   double pan scale, the massleft times the
   distanceleft must equal to massright times
   the distanceright (mldl = mrdr).
                                    5g
       Mass ?
                                    25 g

          15 cm             20 cm


   Calculate the mass needed to be placed
   15 cm away from the fulcrum (pivot) so
   that it will balance the right hand side.
         Do the following Qs
10. In order to have objects balanced on a
    double pan scale, the massleft times the
    distanceleft must equal to massright times
    the distanceright (mldl = mrdr).
                                           50 g
  20 g    20 g

                      5 cm          5 cm

         Distance ?

   Calculate the distance needed away
   from the fulcrum (pivot) so that the
   scale is balance.

				
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