# A.8 and *A.8 - Direct & Inverse Variation

A.8    The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

A.8  The student, given a data set or practical situation, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

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

• The constant of proportionality in a direct variation is represented by the ratio of the dependent variable to the independent variable.
• The constant of proportionality in an inverse variation is represented by the product of the dependent variable and the independent variable.
• A direct variation can be represented by a line passing through the origin.
• Real-world problems may be modeled using direct and/or inverse variations.

·  Practical problems may be represented and solved by using direct variation or inverse variation.

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

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

A.81  Given a situation, including a real-world situation, determine whether a direct variation exists.

·  A.8Given a data set or practical situation, determine whether a direct variation exists.

A.82  Given a situation, including a real-world situation, determine whether an inverse variation exists.

·  A.8Given a data set or practical situation, determine whether an inverse variation exists.

A.83  Write an equation for a direct variation, give a set of data.

·  A.8Given a data set or practical situation, write an equation for a direct variation.

A.85  Graph an equation representing a direct variation, given a set of data.

·  A.8Given a data set or practical situation, graph an equation representing a direct variation.

A.84  Write an equation for an inverse variation, given a set of data.

·  A.8Given a data set or practical situation, write an equation for an inverse variation.

### KEY VOCABULARY

direct variation, inverse variation, set of data, constant of proportionality, dependent variable, independent variable, origin

Updated: Oct 27, 2017