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Concept

Constant of Variation

A constant of variation, also known as a constant of proportionality, is a non-zero constant that relates two variables.

Direct Variation

In a direct variation, the constant of variation

k

represents the ratio of two variables. The ratio remains unchanged when the variables

x

and

y

change.

\frac{y}{x} = k, where x \neq = 0 and y \neq = 0

When the variable

y

is isolated on the left-hand side, the constant of variation

k

defines the slope of the line through the origin that represents the relationship between

x

and

y .

\frac{y}{x} = k \Leftrightarrow y = k x

Inverse Variation

In an inverse variation, the constant of variation

k

is the product of two variables. The product remains the same when the variables

x

and

y

change.

x y = k, where x \neq = 0 and y \neq = 0

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Direct Variation

Inverse Variation