Direct and inverse variation

The  exercise appears under the Algebra I Math Mission. This exercise explores the concepts of direct and inverse variation.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the direct variation equation: This problem provides a list of multiple choice possibilities and asks the student to select which of the options describes two variables that are directly related.Daiv1-too.png
 * 2) Find the inverse variation equation: This problem provides a list of multiple choice possibilities and asks the student to select which of the options describes two variables that are inversely related.Daiv2-too.png

Strategies
Familiarity with word problems and the general equations of direct and inverse variation are encouraged to ensure success on this exercise.
 * 1) Direct variation occurs when an increase in one variable is results with an increase in value of the other variable.
 * 2) Algebraically, direct variation means there is a similar quotient, so look for $$ \frac{x}{y}=k$$ for some constant k.
 * 3) Inverse variation occurs when an increase in one variable is results with a decrease in value of the other variable.
 * 4) Algebraically, inverse variation means there is a similar product, so look for $$x\times y=k$$ for some constant k.

Real-life Applications

 * 1) Direct variation is used in applications such as growth of populations, or value in simple interest situations.
 * 2) Inverse variation is used in work-rate problems, or gravitational pull of celestial bodies based on mass.