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Constant of Variation

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Constant of Variation

Study Guide

Key Definition

The constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities. The formula for direct variation is $y = kx$ where k is the constant of variation.

Important Notes

In direct variation, as one quantity increases, the other also increases.
In indirect variation, as one quantity increases, the other decreases.
The constant of variation is the constant ratio or product between two variables.

Mathematical Notation

$k$ represents the constant of variation

$x$ and $y$ are the variable quantities

Remember to use proper notation when solving problems

Why It Works

The constant of variation provides a predictable relationship between two variable quantities. When this relationship is known, we can predict the value of one variable given the value of the other.

Remember

When working with variations, always identify the constant of variation ($k$) first.

Quick Reference

Direct Variation:$y = kx$

Indirect Variation:$xy = k$

Understanding Constant of Variation

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Video explanation of this concept

Beginner

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Beginner Explanation

In a direct variation, the constant of variation is the ratio of two variable quantities, represented by $y = kx$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If y varies directly as x and y = 15 when x = 24, what is the constant of variation?

Real-World Problem

Question Exercise

Intermediate

Journey Time

If it takes 4 hours at an average speed of 90 km/h to do a certain journey, how long would it take at 120 km/h?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If y varies directly as x and y = 15 when x = 24, find x when y = 25.

Challenge Quiz

Single Choice Quiz

Advanced

In an indirect variation, if x = 4 when y = 90, what is the value of y when x = 120?

Recap

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