#### Math - 2017-18

# 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.8The student, given a data set or practical situation, willanalyzea relation todeterminewhether a direct or inverse variation exists, andrepresenta direct variation algebraically and graphically and an inverse variation algebraically.

**Bloom's Level:** Analyze

*Adopted: 2009*

### 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.

### ESSENTIALS

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

A.8_{1} Given a situation, including a real-world
situation, **determine** whether a
direct variation exists.

·
A.8_{1 }Given a data set or practical
situation, **determine** whether a
direct variation exists.

A.8_{2} Given a situation, including a real-world
situation, **determine** whether an
inverse variation exists.

·
A.8_{2 }Given a data set or practical
situation, **determine** whether an
inverse variation exists.

A.8_{3} **Write**
an equation for a direct variation, give a set of data.

·
A.8_{3 }Given a data set or practical
situation, **write** an equation for a
direct variation.

A.8_{5} **Graph**
an equation representing a direct variation, given a set of data.

·
A.8_{5 }Given a data set or practical
situation, **graph** an equation
representing a direct variation.

A.8_{4} **Write**
an equation for an inverse variation, given a set of data.

·
A.8_{4 }Given 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*