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Santa filled an empty jug of water in science class and calculated the rate at which the jug was being filled. Santa's equation for her calculations was y = 3x, where x represents the number of seconds and y represents the total number of ounces of water.

A) Does the equation represent a proportional relationship? Explain your reasoning.

B) What is the unit rate of change for this situation?

User Cromod
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2 Answers

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A) Yes, the equation y = 3x represents a proportional relationship. A proportional relationship is a type of relationship in which two variables are directly related, meaning that their ratio is constant. In this case, the equation shows that the total number of ounces of water (y) is directly proportional to the number of seconds (x). As x increases, y increases at a constant rate of 3 ounces per second. This is indicated by the coefficient of x (3) in the equation. Therefore, the equation represents a proportional relationship.

B) The unit rate of change for this situation is 3 ounces per second. The unit rate of change is the rate at which one variable changes with respect to another variable, expressed in terms of a specific unit of measurement. In this case, the unit rate of change is the rate at which the total number of ounces of water changes with respect to the number of seconds. Since the equation shows that the total number of ounces of water increases at a rate of 3 ounces per second, the unit rate of change is 3 ounces per second.

User Svenhalvorson
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Proportional relationship equation:

  • y = kx, where k- constant, same time is the unit rate

Part A

  • Given equation is y = 3x, this is of the same format, therefore it represents a proportional relationship.

Part B

  • k = 3, therefore the unit rate is 3 ounces per second.
User Tom Canfarotta
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