#### Math - 2019-20

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

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

*Adopted: 2016*

### 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

· 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*.

### ESSENTIALS

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

· AII.10_{2} Given a data set or practical situation, **write** the equation for a joint
variation.

· AII.10_{1} Given a data set or practical situation, **write** the equation for an inverse
variation.

· AII.10_{3} **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: Aug 23, 2018*