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Chapter 7: Problem 44

What does it mean if two quantities vary directly?

Short Answer

Expert verified
When two quantities vary directly, they are directly proportional to each other meaning they increase or decrease at a set, or constant rate. This relationship can be represented by the equation y = kx, where y and x are the two quantities and k is the constant of proportionality.

Step by step solution

01

Understand Direct Variation

In mathematics, direct variation describes how two variables change in relation to each other. If two quantities vary directly, they change at a consistent rate, meaning the ratio between them stays constant.
02

Characteristics of Directly Varied Quantities

When two quantities vary directly, if one of the quantities increases, the other also increases. Similarly, if one decreases, the other also decreases. This change happens at a constant rate. This is represented mathematically by the equation y = kx, where 'y' and 'x' are the two quantities that directly vary and 'k' is the constant ratio.
03

Illustration

For example, if someone is paid an hourly wage, the person's total income directly varies with the number of hours they work. The more hours they work, the higher their income, maintaining a constant rate (hourly wage).

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