Write and solve inverse variation equations

Learning Objectives Define inverse variation and identify it from a table of values or a word problem. Write the general equation for an inverse variation relationship. Calculate the constant of variation, k, given a pair of values (x, y). Write the specific inverse variation equation that models a given situation. Use an inverse variation equation to find a missing value. Solve real-world problems by applying the principles of inverse variation. Ever noticed that the faster you drive, the less time it takes to get to your destination? 🚗💨 This 'as one thing goes up, the other goes down' relationship is called inverse variation! In this tutorial, you will learn how to recognize, write, and solve equations for inverse variation. This is a powerful mathematical too...

TermDefinitionExample Inverse VariationA relationship between two variables where as one variable increases, the other variable decreases proportionally. Their product remains constant.If it takes 2 people 6 hours to paint a fence, it will take 4 people only 3 hours. The number of people increases, and the time decreases. Constant of Variation (k)The non-zero constant value that is the product of the two variables (x and y) in an inverse variation relationship. It is also called the constant of proportionality.In the relationship where y varies inversely as x, if y = 10 when x = 2, the constant of variation k is 10 * 2 = 20. Equation of Inverse VariationThe general formula that describes an inverse variation relationship.The equation is written as y = k/x, where k is the constant of varia...

The Inverse Variation Equation y = \frac{k}{x} This is the fundamental equation for inverse variation. Use it when you know the constant of variation (k) and want to find the value of one variable (y) given the other (x). The Constant of Variation Formula k = xy This formula is derived from the main equation. Use it to find the constant of variation (k) when you are given a specific pair of corresponding values for x and y. The Inverse Variation Proportion x_1 y_1 = x_2 y_2 This rule is useful for solving problems where you are given an initial set of values (x₁, y₁) and a new value for one variable (x₂ or y₂), and you need to find the corresponding value of the other. It bypasses the need to solve for k first.