**Constant of Variation for Direct Variation:**

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

y = kxHere, ** k is a fixed number** and it is

*. By the above equation, we get the formula*

**known as the constant of variation**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

**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}=1.75So 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} = -0.67Therefore the constant of variation is k=-0.67.