Finding the Constant of Variation

Pre-Algebra · Axiom Academy

EXAMPLE Finding the Constant of Variation Find the constant k in a direct-variation relationship, then use it to predict a new value. Suppose y varies directly with x , and y = 12 when x = 4 . Find the constant of variation k , then use it to find y when x = 7 . Nice work! You found the constant of variation and used it to predict a new value. Remember the moves: Set up the model: " y varies directly with x " always means y = kx . Find the constant: Substitute the known point and solve for k — here . Write the equation: Put k back in to get the full rule, y = 3x . Predict: Substitute any x to find its y — at x = 7 , y = 3(7) = 21 . Direct variation shows up everywhere — distance at a steady speed, pay by the hour, scaling a recipe. The constant k is just the rate at which y grows with x .

This is the written version of the interactive lesson above. See the full Pre-Algebra course.