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Proportional relationships in math refer to the relationship between two variables, y and x, where y is always a constant multiple of x This means that if one quantity increases or decreases, the other quantity does so at a consistent rate, resulting in a straight line when graphed. In other words, as x increases or decreases, y changes proportionally.

When quantities are proportional, their ratios are equal A proportional relationship is a relationship between two quantities where the ratio of one quantity to another remains constant For example, the ratios 2 5 52 and 8 20 208 are proportional

Note that 4 10 104 and 12 30 3012 are equivalent fractions because they both simplify to 2 5 52.

To know if a relationship is proportional, you should look at the ratios between the two variables If the ratio is always the same, the relationship is proportional If the ratio changes, the relationship is not proportional. Two quantities 𝐴 and 𝐵 are proportional, or in proportion, when from one situation to another, both quantities have been multiplied (or divided) by a same number

It follows that the ratios of quantity 𝐴 to quantity 𝐵 are in all situations equivalent. A proportional relationship exists when two quantities increase or decrease at the same rate Simply put, if one value doubles, the other doubles as well—maintaining the same ratio or fraction. Determine whether two quantities presented in authentic problems are in a proportional relationship

Identify, represent, and use proportional relationships.

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