Algebra 1

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Algebra 1

• Direct and InverseVariations

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Objective

• Students will understand the difference between
  direct and inverse variation.
• Students will compute both direct and inverse
  variation.

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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 at a CONSTANT RATE.

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The price of hot dogs varies directly with the
number of hotdogs you buy
You buy hotdogs. x represents the number of
hotdogs you buy. y represents the price you pay.
y kx Lets figure out k, the price per
hotdog. Suppose that when you buy 7
hotdogs, it costs 21. Plug that information
into the model to solve for k. y kx 21
k(7) Now divide both sides by 7 to solve for
k. 7 7 k 3 The price per hotdog is
3. y 3x You could use this model
to find the price (y) for any number of
hotdogs (x) you buy.
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y (price)
y 3x
.
(3,9) When you buy 3 hotdogs, you pay 9
.
(2,6) When you buy 2 hotdogs, you pay 6
.
(1,3) When you buy 1 hotdog, you pay 3
.
x (number of hotdogs)
(0,0) When you buy 0 hotdogs, you pay 0
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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

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Notebook Quiz

• Please take out a sheet of paper and put the
  proper school heading on the upper left of the
  paper.
• You may use your notebook and notes for this quiz.