A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant. In mathematical terms, two variables \( x \) and \( y \) are considered to have a proportional relationship if they can be expressed as:
\[ y = kx \]
where \( k \) is a non-zero constant known as the constant of proportionality. The key characteristics of a proportional relationship include:
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Constant Ratio: For any two corresponding values of \( x \) and \( y \), the ratio \( \frac{y}{x} = k \) remains the same.
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Graphing: When graphed on a coordinate plane, a proportional relationship will produce a straight line that passes through the origin (0,0).
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Direct Variation: Proportional relationships are also referred to as direct variation, meaning that as one quantity increases, the other quantity increases at a consistent rate.
For example, if a recipe requires 2 cups of flour for every 3 cups of sugar, the relationship between cups of flour and cups of sugar is proportional, and the ratios of flour to sugar remain consistent.