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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 a linear 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 using a known pair of 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.
  • 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 on different values in an equation.
  • Restriction
    A limitation on variable values, such as excluding zero in inverse variation to avoid division by zero.
  • Direct Proportion
    A situation where two quantities maintain a constant ratio, increasing or decreasing together.
  • Inverse Proportion
    A situation where the product of two quantities remains constant as one increases and the other decreases.
  • Known Pair of Values
    A specific set of variable values used to determine the constant in a variation equation.
  • Real World Application
    A practical scenario where variation concepts are used to model relationships between measurable quantities.
  • Directly Proportional
    A description for variables that change in the same direction at a constant rate.
  • Inversely Proportional
    A description for variables that change in opposite directions, maintaining a constant product.
  • Linear Equation
    An algebraic statement where variables are to the first power and graph as a straight line.
  • Reciprocal Relationship
    A connection where one variable is the inverse of another, as seen in inverse variation.
  • Multiplicative Constant
    A fixed number multiplied by a variable in direct variation equations.
  • Division by Zero
    An undefined operation that must be avoided, especially in inverse variation equations.
  • Substitution
    The process of replacing a variable with a specific value to solve for another quantity.
  • Graph of Direct Variation
    A straight line through the origin, representing a direct relationship between variables.
  • Graph of Inverse Variation
    A curve that approaches the axes but never touches them, showing an inverse relationship.
  • Opposite Relationship
    A situation where one variable increases as the other decreases, characteristic of inverse variation.
  • Origin
    The point (0,0) on a graph, which direct variation lines always pass through.
  • Product
    The result of multiplying two quantities, which remains constant in inverse variation.