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Direct & Inverse Variation quiz

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  • What is the equation for direct variation?
    The equation for direct variation is y = kx, where k is the constant of variation.
  • How do y and x change in direct variation?
    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 direct variation?
    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 equation relating x and y?
    The equation is y = 5x, since k = 10/2 = 5.
  • What is the value of y when x = 6 in the equation y = 5x?
    y = 30, because 5 × 6 = 30.
  • What is the equation for inverse variation?
    The equation for inverse variation is y = k/x, where k is the constant of variation.
  • How do y and x change in inverse variation?
    In inverse variation, as one variable increases, the other decreases.
  • 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 inverse variation?
    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 equation relating x and y?
    The equation is y = 32/x, since k = 8 × 4 = 32.
  • What is the value of y when x = 2 in the equation y = 32/x?
    y = 16, because 32 ÷ 2 = 16.
  • Why can't x be zero in the equation y = k/x?
    Because division by zero is undefined in mathematics.
  • What is a key step in solving both direct and inverse variation problems?
    A key step is finding the constant of variation k using given values.
  • Give an example of real-world quantities that might use direct or inverse variation.
    Examples include distance, time, speed, price, quantity, volume, and pressure.