Solve variation equations: Set 1

Learning Objectives Translate verbal statements of direct variation into an algebraic equation. Translate verbal statements of inverse variation into an algebraic equation. Calculate the constant of variation, k, given a set of conditions. Write the specific equation that models a given variation relationship. Use a variation equation to find an unknown value when other values are provided. Distinguish between direct and inverse variation from a problem description. Model a real-world scenario using a direct or inverse variation equation. Ever notice that the more you study for a test, the higher your score tends to be? 📈 That relationship is a perfect example of variation! Variation describes how one quantity changes in relation to another. In this tutorial, we will foc...

TermDefinitionExample VariationA mathematical relationship between two or more variables where a change in one variable results in a predictable change in the other(s).The relationship between distance, speed, and time is a form of variation. Direct VariationA relationship between two variables, x and y, where their ratio is a constant. As one variable increases, the other increases proportionally.The cost of buying apples (C) varies directly with the weight of the apples purchased (w). If apples are $2 per pound, the equation is C = 2w. Inverse VariationA relationship between two variables, x and y, where their product is a constant. As one variable increases, the other decreases proportionally.The time (t) it takes to travel a fixed distance varies inversely with your speed (s). The fas...

Direct Variation Formula y = kx Use this formula when a problem states that 'y varies directly as x' or 'y is directly proportional to x'. Here, k is the constant of variation, and k ≠ 0. Inverse Variation Formula y = \frac{k}{x} \quad \text{or} \quad xy = k Use this formula when a problem states that 'y varies inversely as x' or 'y is inversely proportional to x'. Here, k is the constant of variation, and k ≠ 0.