Write and solve inverse variation equations

Learning Objectives Identify an inverse variation relationship from a problem description or a set of data. Write the general equation for an inverse variation relationship. Calculate the constant of variation, k, given a corresponding pair of values. Formulate the specific inverse variation equation for a given scenario. Use an inverse variation equation to find an unknown value. Model and solve real-world problems involving inverse variation. Ever noticed that the more people who share a pizza, the smaller each person's slice gets? 🍕🤔 This is a perfect example of inverse variation in action! This tutorial will guide you through the process of writing and solving inverse variation equations. You will learn how to model relationships where one quantity increases as a...

TermDefinitionExample Inverse VariationA relationship between two variables in which the product is a constant. When one variable increases, the other variable decreases proportionally.If y varies inversely as x, it means as x doubles, y is halved. Constant of Variation (k)The non-zero constant value that represents the product of the two variables in an inverse variation relationship. It is often denoted by the letter 'k'.In the equation y = 12/x, the constant of variation is 12. General Equation of Inverse VariationThe formula that describes any inverse variation relationship before the specific constant is known.The general equation is y = k/x, where k is the constant of variation. Specific Equation of Inverse VariationThe equation that describes a particular inverse variatio...

General Inverse Variation Equation y = \frac{k}{x} Use this formula to represent the relationship that 'y varies inversely as x' or 'y is inversely proportional to x'. Here, k is the constant of variation and k ≠ 0. Formula for the Constant of Variation k = xy To find the constant of variation (k), multiply any given pair of corresponding x and y values. Proportion Form for Solving x_1 y_1 = x_2 y_2 This is a powerful shortcut for solving inverse variation problems. If you know one pair of values (x₁, y₁) and half of another pair (e.g., x₂), you can solve for the missing value (y₂) without first explicitly finding k.