Recognizing direct and inverse variation | Rational expressions | Algebra II | Khan Academy | Summary and Q&A

TL;DR

This video explains how to determine whether relationships between variables are direct or inverse by manipulating and separating the variables in an equation.

Key Insights

• ⌛ Direct variation occurs when one variable is equal to a constant times the other variable.
• ⌛ Inverse variation occurs when one variable is equal to a constant times the reciprocal of the other variable.
• ❓ Relationships between variables can be determined by manipulating and separating the variables in an equation.
• ⚖️ Scaling one variable in a direct variation relationship results in scaling the other variable by the same amount.
• ⚖️ Scaling one variable in an inverse variation relationship results in scaling the other variable by the reciprocal of that amount.
• 📁 Neither direct nor inverse relationships occur when manipulating the equation does not result in a direct or inverse variation pattern.
• 📁 Direct variation implies that both variables increase or decrease together in proportion.

Transcript

I've written some example relationships between two variables-- in this case between m and n, between a and b, between x and y. And what I want to do in this video is see if we can identify whether the relationships are a direct relationship, whether they vary directly, or maybe they vary inversely, or maybe it is neither. So let's explore it a lit... Read More

Questions & Answers

Q: How can we determine whether a relationship between variables is direct or inverse?

To determine the relationship, we can manipulate the equation and separate the variables on different sides. If it is of the form y = kx, it is a direct variation. If it is of the form y = k/x, it is an inverse variation.

Q: What does it mean for two variables to vary directly?

When two variables vary directly, it means that as one variable increases, the other also increases in proportion. They can be expressed as y = kx, where k is a constant.

Q: How can we identify an inverse relationship between variables?

An inverse relationship can be identified if one variable is equal to a constant times the reciprocal of the other variable. This is expressed as y = k(1/x), where k is a constant.

Q: Is it possible for a relationship between variables to be neither direct nor inverse?

Yes, there are cases where the relationship between variables is neither direct nor inverse. In such cases, manipulating the equation and separating the variables will not result in a direct or inverse relationship; instead, the variables may be shifted by a certain amount.

Summary & Key Takeaways

• The video discusses the concept of direct variation, where one variable is equal to a constant times the other variable.

• It also explains the concept of inverse variation, where one variable is equal to a constant times the reciprocal of the other variable.

• The video demonstrates how to identify direct and inverse relationships by manipulating equations and separating the variables on different sides of the equation.