Constant of Variation – Definition & Examples

Constant of Variation for Direct Variation:

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

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

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,

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

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,

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,

Therefore the constant of variation is k=-0.67.