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Chapter 7: Problem 25

What does it mean if two quantities vary directly?

Short Answer

Expert verified
If two quantities vary directly, they are proportional to each other. As one quantity increases, the other does too, and vice versa, in a constant rate or ratio. This relationship can be represented by the equation \(y=kx\), where \(k\) is the constant of variation.

Step by step solution

01

Understanding Direct Variation

Direct variation describes a simple relationship between two variables. If one quantity varies directly as another, it means the quantities are proportional: when one quantity increases, the other increases proportionally, and vice versa. An equation can represent this relation, usually in the form \(y = kx\), where \(k\) is a constant.
02

Visualizing Direct Variation

In the graphical representation, direct variation would appear as a straight line passing through the origin. This is because for all \(x\), \(y\) will be proportionally the same. If \(x\) goes to 0, then \(y\) must also go to 0, aligning with the definition of direct variation.
03

Observing Direct Variation

For example, if the amount one earns (E) is directly proportional to the number of hours worked (h), this relationship can be expressed as \(E=kh\), where \(k\) is the earning rate per hour. So if one works more (increase in h), their earnings will naturally increase (increase in E).

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