Direct and Inverse Variation

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Direct and Inverse Variation

• Take notes when you see this animated pencil.

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Objectives

• Understand the specialized vocabulary
• Know the basic algebraic equations that represent
  direct and inverse variation
• Apply techniques for classifying the types of
  variation

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Direct ProportionDirect VariationDirectly
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).

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Example of Direct Variation

• Equation y 3x
• Variable y is directly proportional to x.
• Tripling x causes y to triple.

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Graph of Direct Variation
y 3x
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Inverse VariationInverse 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).

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Example of Inverse Variation

• Equation y 48/x
• Variable y is inversely proportional to x.
• Tripling x causes y to one third. The product of
  x and y is always 48.

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Graph of Inverse Variation
y 48/x
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Do the following Qs

• 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

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Do the following Qs

• 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.

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Do the following Qs

• 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.

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Do the following Qs

• 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?

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Do the following Qs

• 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 Earths
  equator, you require a width of 38 million
  meters. What is the length of the box?

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Do the following Qs

• 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?

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Do the following Qs

• 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?

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Do the following Qs

• 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).
• Calculate the distance needed away from the
  fulcrum (pivot) so that the 50g object will
  balance the left hand side.

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Do the following Qs

• 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).
• Calculate the mass needed to be placed 15 cm
  away from the fulcrum (pivot) so that it will
  balance the right hand side.

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Do the following Qs

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