Direct and Inverse Variations

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Direct and InverseVariations
Do now if 5 boxes of salt costs 15 dollars, how
much does 4 boxes cost?
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Today we will be able to solve and graph
InverseVariation problems
Do now if 5 boxes of salt costs 15 dollars, how
much does 4 boxes cost?
This is a direct variation problem. We set them
up As a proportion and solve.
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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.
• Can you think of an example
• Of this happening?

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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 with x

X 4 8 2 x
Y 6 3 y -1
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Inverse Variation

• If y varies inversely with x and all
• Products 24

X 4 8 2 X-24
Y 6 3 Y12 -1
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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

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Graphing inverse variations-the graph is a
hyperbola.

• xy c where c is the product of x and y
• Ex xy 12 then

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Example

• If it takes 3 carpenters to frame a house in 8
  weeks, how many weeks will it take four
  carpenters to frame the same house?

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Example

• If it takes 3 carpenters to frame a house in 8
  weeks, how many weeks will it take four
  carpenters to frame the same house?
• (3)(8) (4)(w)
• W 6

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Exit ticket

• Create an inverse variation problem with your
  partner and hand it in on an index card for 3
  bonus points on your next test!