# Constant of Variation – Definition & Examples

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#### Constant of Variation for Direct Variation:

A direct variation between two variables x and y is given by the equation,

y = kx

Here, k is a fixed number and it is known as the constant of variation. By the above equation, we get the formula

k = \frac{y}{x}

In order to find the constant of variation we simply substitute the values for x and y in the above formula.

#### Constant of Variation for Inverse Variation:

An inverse variation between two variables x and y is given by the equation,

y = \frac{k}{x}

Here, k is the constant of variation. By the above equation, we get the formula

k = xy

#### Example 1: Is y=2x a direct variation equation?

Since we have a relationship of the form y = kx we see that it is indeed a direct variation. By comparing the equations, we see that the constant of variation k is equal to 2.

#### Example 2: What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?

We use the formula k = \frac{y}{x} for the case of direct variation. We have that k = \frac{8}{5} and so the constant of variation is k = 1.6.

#### Example 3: For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7?

Substituting the values of y and k in the equation we get that,

xy = k \implies x\times 4 =7 \implies x=\frac{7}{4}=1.75

So the value of x is 1.75.

#### Example 4: What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?

We substitute the values of x and y in the equation below,

k = \frac{y}{x} = \frac{2}{-3} = -0.67

Therefore the constant of variation is k=-0.67.

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