Direct and Inverse Variations

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Direct and InverseVariations
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Direct Variation

• When we talk about a direct variation, we are
  talking about a relationship where as x
  increases, y increases or decreases at a
  CONSTANT RATE.

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Direct Variation
Direct variation uses the following formula
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Direct Variation

• example
• if y varies directly as x and y 10 as x 2.4,
  find x when y 15.
• what x and y go together?

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Direct Variation

• If y varies directly as x and y 10 find x when
  y 15.
• y 10, x 2.4 make these y1 and x1
• y 15, and x ? make these y2 and x2

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Direct Variation

• if y varies directly as x and y 10 as x 2.4,
  find x when y 15

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Direct Variation

• How do we solve this? Cross multiply and set
  equal.

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Direct Variation

• We get 10x 36
• Solve for x by diving both sides by 10.
• We get x 3.6

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Direct Variation

• Lets do another.
• If y varies directly with x and y 12 when x
  2, find y when x 8.
• Set up your equation.

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Direct Variation

• If y varies directly with x and y 12 when x
  2, find y when x 8.

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Direct Variation

• Cross multiply 96 2y
• Solve for y. 48 y.

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Inverse Variation

• Inverse is very similar to direct, but in an
  inverse relationship as one value goes up, the
  other goes down. There is not necessarily a
  constant rate.

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Inverse Variation

• With Direct variation we Divide our xs and ys.
• In Inverse variation we will Multiply them.
• x1y1 x2y2

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Inverse Variation

• If y varies inversely with x and y 12 when x
  2, find y when x 8.
• x1y1 x2y2
• 2(12) 8y
• 24 8y
• y 3

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Inverse Variation

• If y varies inversely as x and x 18 when y 6,
  find y when x 8.
• 18(6) 8y
• 108 8y
• y 13.5