Write inverse variation equations

Learning Objectives Define inverse variation and identify its key characteristics. Identify the general equation for an inverse variation relationship. Calculate the constant of variation, k, given a pair of values (x, y). Write a specific inverse variation equation that models a given relationship. Use an inverse variation equation to find a missing value. Distinguish between an inverse variation equation and a direct variation equation. Ever noticed that the faster you drive, the less time it takes to get to your destination? 🚗 This 'one goes up, the other goes down' relationship is a perfect example of inverse variation! In this tutorial, you will learn how to capture these special relationships using mathematics. We will focus on how to write the specific equ...

TermDefinitionExample Inverse VariationA relationship between two variables, x and y, where as one variable increases, the other variable decreases proportionally. If y varies inversely with x, it means their product is always the same constant value.If it takes 2 people 6 hours to paint a fence, it would take 4 people only 3 hours. As the number of people (x) doubles, the time (y) is halved. 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 = 12/x, the constant of variation 'k' is 12. For any pair of (x, y) values that satisfy this equation, their product will be 12 (e.g., x=2, y=6; 2*6=12). General Equation of...

The General Equation of Inverse Variation y = \frac{k}{x} This is the fundamental formula for any inverse variation. Use this as your starting point when you are asked to write an inverse variation equation. The Formula for the Constant of Variation k = xy This formula is derived from the general equation (by multiplying both sides by x). Use it to find the specific value of 'k' when you are given a corresponding pair of x and y values.