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Direct & Inverse Variation definitions

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  • Direct Variation
    A relationship where two quantities increase or decrease together, modeled by an equation with a constant multiplier.
  • Inverse Variation
    A relationship where one quantity increases as the other decreases, represented by a constant divided by a variable.
  • Constant of Variation
    A fixed value that links two variables in a variation equation, found by substituting known values.
  • Linear Relationship
    A connection between variables that forms a straight line when graphed, such as in direct variation.
  • Proportionality
    A consistent ratio or relationship between two quantities, either direct or inverse.
  • Directly Proportional
    A situation where two variables change in the same direction at a constant rate.
  • Inversely Proportional
    A situation where one variable increases as the other decreases, maintaining a constant product.
  • Equation of Direct Variation
    An expression in the form y = kx, showing two variables changing together with a constant multiplier.
  • Equation of Inverse Variation
    An expression in the form y = k/x, showing one variable changes as the reciprocal of the other.
  • Variable
    A symbol representing a quantity that can change or take different values in an equation.
  • Restriction
    A limitation on variable values, such as not allowing division by zero in inverse variation.
  • Substitution
    The process of replacing variables with known values to solve for unknowns in an equation.
  • Real World Application
    A practical scenario where variation concepts are used to relate meaningful quantities like speed or price.
  • Product
    The result of multiplying two quantities, often constant in inverse variation.
  • Ratio
    A comparison of two quantities, remaining constant in direct variation.
  • Graph of Direct Variation
    A straight line through the origin, showing two variables increasing or decreasing together.
  • Graph of Inverse Variation
    A curve that approaches the axes but never touches them, showing one variable decreases as the other increases.
  • Origin
    The point (0,0) on a graph, where direct variation lines always pass through.
  • Unit Consistency
    The practice of keeping measurement units the same when applying variation equations to real problems.
  • Quantity
    An amount or number that can be measured or counted, often represented by variables in variation.
  • Model
    A mathematical representation of a relationship between variables, such as direct or inverse variation.
  • Application Problem
    A question that uses variation concepts to solve for unknowns in real-life contexts.
  • Multiplier
    A number by which another number is multiplied, as in the constant in direct variation.
  • Reciprocal
    The value obtained by dividing 1 by a number, used in inverse variation equations.