# How to Find the Constant of Variation

The constant of variation is used as a measure to compare the amount of change of one variable with respect to another variable in a functional relationship.

## Step-by-step guide to finding the Constant of Variation

Here’s a step-by-step guide to finding the constant of variation, also known as the constant of proportionality, for a direct variation:

1. Identify the two variables in the relationship and label them as x and y.
2. Write an equation that relates x and y, using the form y = kx, where k is the constant of variation.
3. Choose two pairs of values for x and y, and substitute them into the equation from step 2.
4. Solve for k by dividing the value of y by the value of x for each pair of values.
5. Check that the value of k is the same for both pairs of values. If it is, then k is the constant of variation for the relationship between x and y.

Example: Consider the relationship y = 3x. To find the constant of variation, we choose two pairs of values for x and y: (2,6) and (4,12). Substituting these values into the equation from step 2, we get:

6 = 3 * 2 12 = 3 * 4

Solving for k by dividing y by x for each pair of values, we get:

k = 3 for both pairs of values.

Since the value of k is the same for both pairs of values, we conclude that k = 3 is the constant of variation for the relationship between x and y.

Important note: the constant of variation is only applied to functional relationships that are in the form of a linear relationship, that is, in which the dependent variable changes at a constant rate compared to the independent variable.

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