Write and solve direct variation equations

Learning Objectives Identify a direct variation relationship from a table, graph, or equation. Calculate the constant of variation (k) from a given set of values. Write the specific direct variation equation that models a given relationship. Use a direct variation equation to find an unknown value. Solve real-world problems by modeling them with direct variation equations. By the end of a this lesson, students will be able to distinguish between a direct variation and a general linear relationship. Ever notice how the more songs you download, the more storage space you use? 📱 That predictable relationship is a perfect example of direct variation! In this tutorial, you will learn how to recognize, write, and solve equations for a special type of linear relationship called d...

TermDefinitionExample Direct VariationA relationship between two variables, typically x and y, where y is a constant multiple of x. As x increases, y increases by the same factor, and as x decreases, y decreases by the same factor.If you earn $15 per hour, your total earnings (y) vary directly with the number of hours you work (x). The relationship is y = 15x. Constant of Variation (k)The non-zero constant number that relates the two variables in a direct variation. It is often referred to as the constant of proportionality.In the equation y = 15x, the constant of variation 'k' is 15. Independent Variable (x)The variable that is changed or controlled in a relationship. It is the 'input' value.In y = 15x, the number of hours worked (x) is the independent variable becaus...

The Direct Variation Equation y = kx This is the fundamental formula for direct variation, where 'y' is the dependent variable, 'x' is the independent variable, and 'k' is the constant of variation. Use this to model any direct variation relationship. Finding the Constant of Variation k = y/x To find the constant 'k', divide the y-value by its corresponding x-value. This works for any non-zero pair of (x, y) values in the relationship. Proportion Form y₁/x₁ = y₂/x₂ Since the ratio y/x is constant for any pair of points (x₁, y₁) and (x₂, y₂) in a direct variation, you can set their ratios equal. This is useful for solving for an unknown value without first finding 'k'.