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7.6 – Inverse Variation
Key Terms
 Direct Variation – A relationship in which one variable is a constant multiple of the other variable.
 You can say that y varies directly with x and write y = kx, where k is a constant.
 Input – A number that is entered into a function.
 The input variable in a function is the independent variable.
 Inverse Variation – A relationship in which quantities change inversely — as one quantity gets bigger, the other one gets smaller.
 Output – The result of a function.
 The output variable in a function is the dependent variable.
Notes
Direct Variation 
Inverse Variation 
 A proportional relationship between two variables whose ratio is a constant.
 To find the constant:
 Input and output change in the same way proportionally.
 As input increases, output increases.
 As input decreases, output decreases.
 If you double the input, the output doubles.
 The size changes, but the shape does not.
 The equation is linear, so the graph is a line.

 A proportional relationship between two variables whose product is a constant.
 To find the constant:
 Input and output change in opposite ways proportionally.
 As input increases, output decreases.
 As input decreases, output increases.
 If you double the input, the output is halved.
 The shape changes, but the size does not.
 The equation is rational, so the graph is a curve.

Direct Variation Vs Inverse Variation 

 Animation: Direct Variation
 Animation: Inverse Variation

Examples
 Ex 1. Find the constant.
 Direct variation: width = 10, height = 5
 Width is the input and height is the output.
 , so
 Divide both sides by 10:
 Answer:

 Ex 2. Ex 2. Find the constant.
 Inverse variation: width = 10, height = 11
 Width is the input and height is the output.
 , so
 Multiply 10 on both sides:
 Answer:

Important!
Practice (Apex Study 7.6)
 Try practice problems on Pg 14
 Mandatory: write and answer problems on Pg15
 1 Quiz
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