Insert Lesson Title Here Course 2 Identifying IV QUESTION What are the three ways to show inverse...
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Insert Lesson Title Here Course 2 Identifying IV QUESTION What are the three ways to show inverse variation?
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Transcript of Insert Lesson Title Here Course 2 Identifying IV QUESTION What are the three ways to show inverse...
Insert Lesson Title Here
Course 2
Identifying IV
QUESTIONWhat are the three
ways to show inverse variation?
3 ways to show inverse variations:
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Course 2
Identifying IV
* by a table
* by an equation
* by a graph
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Course 2
Identifying IV
QUESTIONHow can a table show
inverse variation?
Table
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Identifying IV
- either x increases and y decreases, or x decreases and y increases (vary inversely)
- the product of each x and corresponding y is the same
x 30 15 5
y 1 2 6
Example of Indirect Variation:
1. As x increases (3, 12, 48), y decreases 8, 2, 1/3).
2. What is the constant of variation of the table above?
3 • 8 = k or k = 24
12 • 2 = k or k = 24
48 • 1/3 = k or k =24 Note k stays constant.
x y
3 8
48 1/3
12 2
k xy
Course 2
Identifying IV
Do these tables show IV?
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Identifying IV
x 1 ½ ¼
y 4 8 16
x -2 0 2
y 1 0 -1
x 4.5 3 0.5
y 2 3 18
x -24 -12 -8
y -½ -1 -1 ½
YES
NOYES
YES
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Course 2
Identifying IV
QUESTIONHow can an equation
show inverse variation?
Equation
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Identifying IV
- written in the form: y = k/x
- other possible form: xy = k
- k = 0
Example: y = 4/x
Do these equations show IV?
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Identifying IV
y = 6x
2y = x y/8 = 1/x
y = 3.4/xNO
NO
YES
YES
xy = -12YES y = -4/x + 2 NO
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Identifying IV
QUESTIONHow can a graph show
inverse variation?
GraphInsert Lesson Title Here
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Identifying IV
- curved line formed by connected points will NOT go through the origin
- approaches the axes but never crosses them
Do these graphs show IV?
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Identifying IV
NO YES
NO YES
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Identifying IV
QUESTIONWhat is the proportion for indirect or inverse
variation?
Proportion:
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Identifying IV
1 2
2 1
x y
x y
1. Arrange one pair as the numerator of one ratio and the denominator of the other. 2. Arrange the other pair in the same manner.
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Identifying IV
VOCABULARY
KK II MMinverse
variation- one variable increases, other decreases- product of variables x and y is constant
y = k/x
Is this an inverse variation?
Course 2
Identifying IV
12 3 4 ( 3)y
x
3x
y
2y
x
4y
x
1
8
y
x
5y x
12xy
1 3y x
2
24y
x
