Write and solve direct variation equations

Learning Objectives Define direct variation and identify the constant of variation, k. Translate verbal descriptions of direct variation into the algebraic equation y = kx. Solve for the constant of variation given a single pair of corresponding values for the variables. Write the specific direct variation equation that models a given relationship. Use a direct variation equation to find an unknown value when another is provided. Distinguish a direct variation relationship from a general linear relationship by recognizing its graph must pass through the origin. Ever wonder why doubling the ingredients in a recipe doubles the servings? 🧑‍🍳 That perfectly predictable relationship is a real-world example of direct variation! This tutorial will demystify the concept of direct...

TermDefinitionExample Direct VariationA relationship between two variables, typically x and y, in which their ratio is a non-zero constant. As one variable increases, the other increases by the same factor, and as one decreases, the other decreases by the same factor.If y varies directly as x, and y = 10 when x = 2, then y = 20 when x = 4. The ratio y/x is always 5. Constant of Variation (k)The non-zero constant ratio in a direct variation, denoted by the letter 'k'. It represents the factor that links the two variables.In the equation y = 3x, the constant of variation is k = 3. This means y is always 3 times the value of x. Dependent VariableThe variable (usually y) whose value depends on the value of the independent variable. It is the output of the function.In the scenario &#...

The Direct Variation Equation y = kx This is the fundamental equation 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. Formula for the Constant of Variation k = \frac{y}{x}, \text{ where } x \neq 0 To find the constant 'k', divide any corresponding non-zero value of y by its x value. This is the first step in finding the specific equation for a relationship. The Proportion Form \frac{y_1}{x_1} = \frac{y_2}{x_2} Since the ratio y/x is constant for any pair of points (x₁, y₁) and (x₂, y₂) in a direct variation (excluding the origin), this proportion can be used to solve for an unknown value without...