The diagram below shows the relationship between the number of cans of chemical A and the number of cans of chemical B needed to form a chemical mixture.
In the equations below, y represents the number of cans of chemical B, and x represents the number of cans of chemical A. Which equation represents the proportional relationship in this diagram?
A. y = 2.5x
B. x = 2.5y
C. y = 1.5 + x
D. x = 1.5y
The answer is A. y = 2.5x. This equation represents a proportional relationship because the number of cans of chemical B is directly proportional to the number of cans of chemical A, with a ratio of 2.5.
explain
In a proportional relationship, two quantities are related in such a way that they always have the same ratio or proportion. In this case, the diagram shows that as the number of cans of chemical A increases, the number of cans of chemical B also increases.
The equation y = 2.5x represents this relationship because it states that the number of cans of chemical B (y) is equal to the number of cans of chemical A (x) multiplied by 2.5. This means that for every increase of 1 can of chemical A, there will be an increase of 2.5 cans of chemical B.
Option B (x = 2.5y) does not represent a proportional relationship because it states that the number of cans of chemical A is equal to the number of cans of chemical B multiplied by 2.5. This means that for every increase of 1 can of chemical B, there will be an increase of 2.5 cans of chemical A, which does not match the information given in the diagram.
Option C (y = 1.5 + x) and option D (x = 1.5y) do not represent proportional relationships either because they include addition or subtraction (option C) and division (option D) in addition to multiplication. In a proportional relationship, the two quantities are only related by multiplication or division.
To determine which equation represents the proportional relationship in the given diagram, we need to look for a constant ratio between the number of cans of chemical A (x) and the number of cans of chemical B (y).
In other words, we're trying to find an equation of the form y = kx, where k is a constant.
Let's look at the equation choices one by one:
A. y = 2.5x
This equation shows a constant ratio of 2.5 between y and x, indicating that for every 2.5 cans of chemical A, we need 1 can of chemical B. This equation represents a proportional relationship.
B. x = 2.5y
This equation represents the inverse relationship, where for every 2.5 cans of chemical B, we need 1 can of chemical A. It is not the same as the given diagram, so it does not represent a proportional relationship.
C. y = 1.5 + x
This equation includes a constant term (1.5), indicating that there is an offset or additional amount needed for chemical B beyond what is proportional to chemical A. It does not represent a proportional relationship.
D. x = 1.5y
Similar to choice B, this equation represents an inverse relationship where for every 1.5 cans of chemical B, we need 1 can of chemical A. It is not the same as the given diagram, so it does not represent a proportional relationship.
Therefore, the equation that represents the proportional relationship in this diagram is choice A:
A. y = 2.5x