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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 you describe the relationship between two variables in direct variation?
    In direct variation, as one variable increases or decreases, the other does the same.
  • What does the constant of variation (k) represent in direct variation?
    The constant of variation (k) is the fixed value that connects the two variables in the equation y = kx.
  • How do you find the constant of variation in a direct variation problem?
    You substitute the given values of x and y into y = kx and solve for k.
  • What does it mean if y varies directly as x?
    It means y is directly proportional to x, or y = kx for some constant k.
  • 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 inverse variation relate to each other?
    In inverse variation, as one variable increases, the other decreases, and vice versa.
  • How do you find the constant of variation in an inverse variation problem?
    You substitute the given values of x and y into y = k/x and solve for k.
  • What does it mean if y varies inversely as x?
    It means y is inversely proportional to x, or y = k/x for some constant k.
  • What restriction exists for the variable x in inverse variation?
    x cannot be zero in inverse variation because division by zero is undefined.
  • If y = 10 when x = 2 in a direct variation, what is the equation relating x and y?
    First, k = 10/2 = 5, so the equation is y = 5x.
  • If y = 8 when x = 4 in an inverse variation, what is the equation relating x and y?
    First, k = 8 × 4 = 32, so the equation is y = 32/x.
  • How do you solve for y in a direct variation equation once you know k and x?
    You multiply k by x, using the equation y = kx.
  • How do you solve for y in an inverse variation equation once you know k and x?
    You divide k by x, using the equation y = k/x.
  • What are two phrases that indicate a direct variation relationship?
    The phrases 'varies directly as' and 'is directly proportional to' both indicate direct variation.