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Direct variation

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College Algebra

Definition

Direct variation describes a linear relationship between two variables where one variable is a constant multiple of the other. Mathematically, it is expressed as $y = kx$, where $k$ is the constant of variation.

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5 Must Know Facts For Your Next Test

  1. In direct variation, as one variable increases, the other variable increases proportionally.
  2. The graph of a direct variation equation is a straight line passing through the origin (0,0).
  3. The constant of variation $k$ represents the slope of the line in a direct variation equation.
  4. If $y$ varies directly with $x$, then $\frac{y}{x} = k$ for all pairs $(x, y)$.
  5. In problems involving direct variation, solving for $k$ can help find unknown values given one pair of variables.

Review Questions

  • What is the general form of a direct variation equation?
  • How does changing the value of $k$ affect the graph of a direct variation?
  • If $y$ varies directly with $x$, and you know that when $x = 3$, $y = 9$, what is the constant of variation?
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