Distinguish between direct and inverse variation

The  exercise appears under the Algebra II Math Mission. This exercise practices finding if two-variable equations show direct or inverse variation.

Types of Problems
There is one type of problems in this exercise:


 * 1) Find the equation shows that shows direct/inverse variation: This problem provides a list of multiple choice possibilities and asks the student to select which of the options has the equation with direct/inverse variation. Distinguish between direct and inverse variation.PNG

Strategies
Knowledge of the differences between direct and inverse variation is essential 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.