Free Direct Variation calculator with clear step-by-step results.
Two quantities vary directly when their ratio never changes: y/x is a fixed constant k. This calculator recovers k from one known (x, y) pair by dividing y by x, then uses y = kx to predict the output at any other x. Because the relationship is purely multiplicative, multiplying x by any factor multiplies y by exactly the same factor — which is why the x scale factor and the ratio of the two y values always agree. A zero known x is rejected because k would be undefined.
Constant of variation
k = y / x (from the known pair)
Prediction
y_target = k x x_target
Divide y by x for every pair you have. If the quotient is the same each time, the data varies directly and that quotient is k. If the quotient drifts, the relationship is not direct variation.
k is the amount y changes for each one-unit increase in x, and it is the slope of the line y = kx through the origin. In a unit-price problem k is the price per item; in a distance problem at constant speed k is the speed.
k is defined as y divided by x, so a known x of zero leaves k undefined. Direct variation always passes through the origin, which means the point (0, 0) carries no information about k.