48 Direct and Inverse Variation

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4-8 Direct and Inverse Variation
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Direct Variation

• y kx where k does not 0
• k is known as the constant of variation.
• y varies directly as x
• OR
• y is directly proportional to x

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Example 1

• A car uses 8 gallons of gasoline to travel 290
  miles. How much gasoline will the car use to
  travel 400 miles.

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Example 2

• y varies directly as x
• a) If y 6 when x 8 find y when x 12
• b) If y 3 when x 9 find y when x 40.5

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Example 3

• Kyles wages vary directly as the number of
  hours that he works. If his wages for 5 hours
  are 29.75, how much will they be for 30 hours?

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Inverse Variation

• y k/x
• y varies inversely as x
• k is the constant of variation

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Example 4

• Suppose y varies inversely as x when x 80, y
  2. Find y when x 16.

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What is another way to write y k/x

• We can write this same equation without the
  fraction as xy k
• Is this true for the last example?

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Example 5

• If the tension on a violin string is constant,
  the frequency of a note varies inversely as the
  length of the string. When the length of a
  violin string is 75cm the frequency is 512Hz.
  What length do we want a string to be that
  produces a frequency of 640Hz?

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Example 6

• What about a frequency of 328Hz from the previous
  example?

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Example 7

• A 200lb. Weight is located 5 feet from the
  fulcrum. How far from the fulcrum should 125lbs.
  Be placed to balance the lever?

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Classwork

• Pg 242 1,4,5-11
• Together.
• HW
• Pg 243 12-34 all