Proportional vs. Non-proportional

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What is a proportional relationship?

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A proportional relationship is one where two quantities maintain a constant ratio or rate. For example, if y is proportional to x, then y = kx for some constant k.

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CCSS.7.RP.A.2A

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What is a non-proportional relationship?

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A non-proportional relationship is one where the ratio between two quantities is not constant. This means that as one quantity changes, the other does not change at a consistent rate.

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CCSS.7.RP.A.2D

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CCSS.7.RP.A.2A

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CCSS.7.RP.A.2A

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CCSS.7.RP.A.2A

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CCSS.7.RP.A.2A

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What does it mean if a pricing structure is non-proportional?

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It means that the cost per item changes as the quantity increases. For example, buying 4 items for $8 and 10 items for $15 shows a non-proportional relationship.

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CCSS.7.RP.A.2A

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If Heba knows 5 songs after 1 lesson and 10 songs after 2 lessons, is this proportional?

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No, it is non-proportional because the increase in songs is not consistent after each lesson.

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CCSS.7.RP.A.2A

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What is the significance of a constant rate in a proportional relationship?

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A constant rate means that for every unit increase in one quantity, there is a consistent unit increase in the other quantity, maintaining the same ratio.

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CCSS.7.RP.A.2D

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If Javon charges $10 per hour, what type of relationship does this represent?

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This represents a proportional relationship because the total charge increases consistently with the number of hours worked.

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CCSS.7.RP.A.2A