# AII.10 and *AII.10 - Direct, Inverse, & Joint Variation

AII.10    The student will identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations.

AII.10  The student will represent and solve problems, including practical problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

Bloom's Level:  Analyze

### BIG IDEAS

• I can determine how much time a diver will need to safely ascend to the surface from various depths, figure how driving speed effects travel time and gallons of gas in tank, and find how light intensity oscillates in relation to distance.
• I will be able to distinguish between situations where one value increases or decreases in proportion to the other value increasing or decreasing and those situations where one value changes in reverse to the other value changing.

### UNDERSTANDING THE STANDARD

• Real-world problems can be modeled and solved by using inverse variation, joint variation, and a combination of direct and inverse variations.
• Joint variation is a combination of direct variations.

·  Practical problems can be represented and solved by using direct variation, inverse variation, joint variation, and a combination of direct and inverse variations.

·  A direct variation represents a proportional relationship between two quantities. The statement “y is directly proportional to x” is translated as y = kx.

·  The constant of proportionality (k) in a direct variation is represented by the ratio of the dependent variable to the independent variable and can be referred to as the constant of variation.

·  A direct variation can be represented by a line passing through the origin.

·  An inverse variation represents an inversely proportional relationship between two quantities. The statement “y is inversely proportional to x” is translated as y = .

·  The constant of proportionality (k) in an inverse variation is represented by the product of the dependent variable and the independent variable and can be referred to as the constant of variation.

·  The graph of an inverse variation is a rational function.

·  Joint variation is a combination of direct variations. The statement “y varies jointly as x and z” is translated as y = kxz.

·  The value of the constant of proportionality is typically positive when applied in practical situations.

### ESSENTIALS

Direct, Inverse, Joint

All.101  Translate “y varies jointly as ax and z” as y=kxz

·  AII.102  Given a data set or practical situation, write the equation for a joint variation.

All.102  Translate “y is directly proportional to x” as y= kx

All.103  Translate “y is inversely proportional to x”as y = k/x.

·  AII.101  Given a data set or practical situation, write the equation for an inverse variation.

All.104  Given a situation, determine the value of the constant of proportionality.

All.105  Set up and solve problems, including real-world problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

·  AII.103  Solve problems, including practical problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

### KEY VOCABULARY

inverse variation, joint variation, direct variation, constant of proportionality, varies jointly, varies directly, varies inversely, combination of variations

Updated: Oct 27, 2017