Define direct variation in math.
Understand the Problem
The question is asking for the definition of direct variation in mathematical terms, specifically how one variable relates to another when they vary directly.
Answer
Direct variation means $y = kx$, where $k$ is a constant.
Answer for screen readers
Direct variation means that two variables are related proportionally, expressed as $y = kx$ where $k$ is a constant.
Steps to Solve
- Definition of Direct Variation
Direct variation describes a relationship between two variables in which they increase or decrease together. This means that if one variable increases, the other variable increases proportionally, and if one decreases, the other decreases proportionally.
- Mathematical Expression
The relationship can be expressed mathematically as:
$$ y = kx $$
where $y$ is the dependent variable, $x$ is the independent variable, and $k$ is a non-zero constant known as the constant of variation.
- Constant of Variation
The constant $k$ represents the rate at which $y$ changes with respect to $x$. It can be calculated by dividing $y$ by $x$ whenever $x \neq 0$:
$$ k = \frac{y}{x} $$
- Example of Direct Variation
For instance, if $y = 3x$, this indicates that for every unit increase in $x$, $y$ increases by 3 units. If $x = 2$, then $y = 3(2) = 6$.
Direct variation means that two variables are related proportionally, expressed as $y = kx$ where $k$ is a constant.
More Information
In direct variation, variables are linked by multiplication. As one variable changes, the other does so at a constant rate, providing a predictable linear relationship.
Tips
- Confusing direct variation with inverse variation, where one variable increases while the other decreases.
- Forgetting that $k$ cannot be zero in direct variation.
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