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Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. This relationship can be written in the equation form \( y = kx \), where \( k \) is a constant. In direct variation, as one variable increases, the other variable increases proportionally. If you double \( x \), then \( y \) will also double, provided \( k \) remains the same. Examples of direct variation include scenarios like speed and distance, where doubling the speed doubles the distance covered in the same amount of time.

Equations can represent different types of relationships between variables. In the context of variation, we primarily look at direct and inverse variations:
- Direct Variation: The equation is in the form \( y = kx \). Here, \( k \) is a non-zero constant. For example, if \( y = 3x \), it means that for every unit increase in \( x \), \( y \) increases by 3 units.
- Inverse Variation: The equation is in the form \( y = \frac{k}{x} \). Here, \( k \) is also a non-zero constant. For instance, if \( y = \frac{5}{x} \), as given in the exercise, it means that as \( x \) increases, \( y \) decreases proportionally, and vice versa.
Understanding these forms is crucial for identifying the type of variation and how changes in one variable affect the other.

Identifying whether an equation represents direct or inverse variation involves recognizing its form.
- Step 1: Look at the structure of the equation. Is one variable a multiple of the other, or is one variable inversely proportional to the other (i.e., one variable is in the denominator)?
- Step 2: Compare the equation with the standard forms of direct (\( y = kx \)) and inverse variation (\( y = \frac{k}{x} \)).
- Step 3: Check for constants that match these patterns. For example, in the given problem, \( y = \frac{5}{x} \) matches the inverse variation form because \( y \) is written as \( 5 \) divided by \( x \). Therefore, we conclude that the equation represents an inverse variation.
By carefully analyzing the equation and comparing it to these standard forms, you can easily identify the type of variation represented.