Exploring Direct Variation

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Exploring Direct Variation

• 3.2

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Direct variation

• y kx or y/x k where k 0
• Whenever two variables have a constant ratio they
  are said to show direct variation

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Example (employment)

• Do earnings vary directly with hours worked?

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Example One

• Check whether the pairs have a constant ratio by
  setting up a ratio of
• earnings/hrs works
• 11.50/2 5.75
• 17.25/3 5.75
• 23.00/4 5.75
• 28.75/5 5.75

• The constant of variation in dollars is 5.75
• So let e earnings and h hrs we get
• e 5.75h

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Example Two

• Do prices of different containers of juice vary
  directly with their sizes? If so give the
  constant of variation and write an equation.

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• 10/.4 .04
• 48/1.99 .04
• 64/1.69 .03
• 64/2.99 .05
• The data does not have a constant ratio therefore
  it does not show direct variation

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Homework

• P. 109 1-10, 13-14, 18-21