Direct%20and%20Inverse%20Variations

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Direct and InverseVariations
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Direct Variation

•  

3
Which of these tables models direct variation?
If so, write an equation.
 
 
NO
 
4
Tell if the following graph is a Direct Variation
or not.
Yes (straight line through the origin!)
No
No
No
5
exampleIf y varies directly as x and y 10 as
x 2.4, find x when y 15.
10x 36 x3.6
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If y varies directly with x and y 12 when x
2, find y when x 8.
Cross multiply 96 2y Solve for y. 48
y.
7
The Weight (V) of an object on Venus varies
directly as its weight (E) on Earth. A person
weighing 120 lb on Earth would weigh 106 lb on
Venus. How much would a person weighing 150 lb
on Earth weigh on Venus?
 
150(106) 120y 15900 120y 132.5 pounds 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.
• The values of x and y always multiply to give the
  same value.

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Graphs of inverse variation
 
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Which of these tables models indirect variation?
If so, write an equation.
 
NO
 
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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

14
In kick boxing, it is found that the force, f,
needed to break a board, varies inversely with
the length, l, of the board.  If it takes 5 lbs
of pressure to break a board 2 feet long, how
many pounds of pressure will it take to break a
board that is 6 feet long?
 
106x 1.67 lbsx