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Direct & Inverse Variation quiz

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  • What is the general equation for direct variation?
    The general equation for direct variation is y = kx, where k is the constant of variation.
  • How do the variables in a direct variation relationship change with respect to each other?
    In direct variation, as one variable increases or decreases, the other does the same.
  • What does it mean if y is directly proportional to x?
    It means y varies directly as x, following the equation y = kx.
  • How do you find the constant of variation (k) in a direct variation problem?
    Substitute the given values of x and y into y = kx and solve for k.
  • If y = 10 when x = 2 in a direct variation, what is the value of k?
    k = 10 / 2 = 5.
  • Given the direct variation equation y = 5x, what is y when x = 6?
    y = 5 × 6 = 30.
  • What is the general equation for inverse variation?
    The general equation for inverse variation is y = k / x, where k is the constant of variation.
  • How do the variables in an inverse variation relationship change with respect to each other?
    In inverse variation, as one variable increases, the other decreases, and vice versa.
  • What does it mean if y is inversely proportional to x?
    It means y varies inversely as x, following the equation y = k / x.
  • How do you find the constant of variation (k) in an inverse variation problem?
    Substitute the given values of x and y into y = k / x and solve for k.
  • If y = 8 when x = 4 in an inverse variation, what is the value of k?
    k = 8 × 4 = 32.
  • Given the inverse variation equation y = 32 / x, what is y when x = 2?
    y = 32 / 2 = 16.
  • Why can't x be zero in an inverse variation equation?
    Because division by zero is undefined in mathematics.
  • What is the main difference between direct and inverse variation?
    In direct variation, both variables change in the same direction; in inverse variation, they change in opposite directions.
  • What are some real-world examples where direct or inverse variation might be used?
    Examples include price and quantity, distance and time, or time and speed.