Direct Variation Calculator

What is Direct Variation?

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. This relationship can be expressed with the equation:

y = kx

Where:

• y is the dependent variable
• x is the independent variable
• k is the constant of variation (a fixed number)

How to Use This Calculator

1. Enter the values for x and y. These are any two corresponding values from your direct variation relationship.
2. Optionally, if you know the constant of variation k, you can enter it in the k field.
3. Click the "Calculate" button.
4. The calculator will:
• Calculate the constant of variation k if not provided
• Predict the value of y for the given x using the equation y = kx
• Verify that the relationship maintains direct variation

Example

Suppose you know that when x = 3, y = 12. You can use this calculator to find the constant of variation:

1. Enter x = 3 and y = 12
2. The calculator will show k = 4
3. This means the equation is y = 4x
4. You can then verify this by checking if 4 × 3 equals 12 (which it does)

Applications of Direct Variation

Direct variation appears in many real-world scenarios:

• Distance traveled at a constant speed (d = rt)
• Cost of items at a fixed price per unit
• Relationship between weight and volume of water
• Simple interest calculations