Direct Variation Calculator | Find Constant of Variation k (y = kx)

Calculate direct variation between two variables. Find the constant of proportionality k, predict y values, and solve y = kx problems instantly.

Calculate direct variation instantly with our free calculator. Find the constant k from a known x,y pair and predict y for any new x using the formula y = kx.

Key Takeaway

Use the free Direct Variation Calculator to calculate direct variation between two variables. find the constant of proportionality k, predict y values, and solve y = kx problems instantly. Get instant results with step-by-step explanations.

How to Use the Direct Variation Calculator

Enter a known x value from the direct variation relationship.
Enter the corresponding known y value.
The calculator finds k = y/x automatically.
Enter a new x value to predict the corresponding y using y = kx.

The Formula

In direct variation, y varies directly as x: y = kx, where k is the constant of proportionality. Given a known pair (x, y), compute k = y/x. Then predict any y from y = k × new_x.

Variable Definitions

y: The dependent variable that varies directly with x
x: The independent variable
k: The constant of proportionality (variation constant): k = y/x
∝: Symbol for "varies directly as": y ∝ x means y = kx

Direct Variation: y = 12 when x = 4

Find k and predict y when x = 5.

Step 1: Given y = 12 when x = 4, compute k = y/x = 12/4 = 3.
Step 2: The direct variation equation is y = 3x.
Step 3: To predict y when x = 5: y = 3 × 5 = 15.
Step 4: Verify proportionality: 12/4 = 15/5 = 3. The ratio is constant.

Frequently Asked Questions

What is direct variation?

Direct variation is a relationship between two variables where one is a constant multiple of the other, expressed as y = kx. As x increases, y increases proportionally, and vice versa.

How do I find the constant of variation k?

Divide any known y value by its corresponding x value: k = y/x. This ratio is the same for every pair in a direct variation relationship.

What does the graph of direct variation look like?

The graph is a straight line passing through the origin (0,0) with slope equal to the constant k. A positive k means the line rises; a negative k means it falls.

Can k be negative?

Yes. A negative k means y and x move in opposite directions. For example, if k = -3, then y = -3x, so when x increases, y decreases.

What are real-life examples of direct variation?

Examples include: distance traveled at constant speed (d = vt), cost of items at fixed price (C = np), Ohm's law (V = IR), and Hooke's law (F = kx).

How is direct variation different from inverse variation?

In direct variation (y = kx), both variables increase together. In inverse variation (y = k/x), one increases while the other decreases. The product xy is constant in inverse variation, while the ratio y/x is constant in direct variation.

Can I use this calculator with zero?

If x = 0, then y must also be 0 for direct variation (since y = k×0 = 0). However, k = y/x is undefined when x = 0, so you need a non-zero x value to find k.

What if I have multiple data points?

For direct variation, k should be the same for all pairs. Compute k = y/x for each pair. If they are all equal (or very close), the relationship is truly direct variation.

Direct Variation Calculator – Guide & Formulas