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# Identifying Proportional Relationships

A proportional relationship exists between two variables if they have a constant ratio. In other words, as one variable increases, the other variable also increases or decreases by the same proportion.

• Identifying Proportional Relationships
• Solved Examples
• Formula
• FAQs

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## Identifying Proportional Relationships

A proportional relationship exists between two variables if they have a constant ratio. In other words, as one variable increases, the other variable also increases or decreases by the same proportion.

To identify proportional relationships, you can follow these steps:

Look at the given data or equation and identify the two variables involved.

Find the ratio between the two variables for each set of data or in the equation.

Check if the ratio is the same for all sets of data or in the equation. If it is the same, then the variables have a proportional relationship.

For example, let’s consider the data below:

x y

1 2

2 4

3 6

4 8

To identify whether x and y have a proportional relationship, we can calculate the ratio y/x for each set of data:

y/x = 2/1 = 2

y/x = 4/2 = 2

y/x = 6/3 = 2

y/x = 8/4 = 2

Since the ratio y/x is the same for all sets of data, we can conclude that x and y have a proportional relationship. In this case, we can say that y is directly proportional to x with a constant of proportionality 2.

Another example is the equation y = 0.5x. To identify if x and y have a proportional relationship, we can calculate the ratio y/x as follows:

y/x = 0.5

Since the ratio y/x is the same for all values of x, we can conclude that x and y have a proportional relationship. In this case, we can say that y is directly proportional to x with a constant of proportionality 0.5.

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## Solved Examples

Sure, here are some solved examples to explain how to identify proportional relationships:

Example 1: Determine if the variables x and y have a proportional relationship for the following data:

x y

2 4

4 6

6 8

8 10

Solution:

To check if x and y have a proportional relationship, we need to find the ratio between y and x for each set of data:

y/x = 4/2 = 2

y/x = 6/4 = 1.5

y/x = 8/6 = 1.33

y/x = 10/8 = 1.25

Since the ratios are not the same for all sets of data, x and y do not have a proportional relationship.

Example 2: Determine if the variables a and b have a proportional relationship for the following equation:

a/3 = b/6

Solution:

To check if a and b have a proportional relationship, we need to simplify the equation by cross-multiplying:

6a = 3b

Dividing both sides by 3, we get:

2a = b

Since a and b have a constant ratio of 2, they have a proportional relationship.

Example 3: Determine if the variables p and q have a proportional relationship for the following data:

p q

2 6

4 12

6 18

8 24

Solution:

To check if p and q have a proportional relationship, we need to find the ratio between q and p for each set of data:

q/p = 6/2 = 3

q/p = 12/4 = 3

q/p = 18/6 = 3

q/p = 24/8 = 3

Since the ratios are the same for all sets of data, p and q have a proportional relationship with a constant ratio of 3.

## Identifying Proportional Relationships FAQS

##### What is a proportional relationship?

A proportional relationship is a relationship between two variables where their ratio is constant. In other words, as one variable increases or decreases, the other variable changes in proportion to maintain a constant ratio.

##### How do you identify a proportional relationship from a table of values?

To identify a proportional relationship from a table of values, calculate the ratio of the two variables for each set of data. If the ratios are the same for all sets of data, then the variables have a proportional relationship with a constant ratio.

##### How do you identify a proportional relationship from an equation?

To identify a proportional relationship from an equation, rearrange the equation to y/x = k form, where k is a constant. If the ratio of y to x is constant, then the variables have a proportional relationship.

##### Can a proportional relationship have a negative ratio?

Yes, a proportional relationship can have a negative ratio. This means that as one variable increases, the other variable decreases in proportion to maintain a constant ratio.

##### How do you find the constant of proportionality?

The constant of proportionality, denoted by k, is the constant ratio between the two variables in a proportional relationship. To find the constant of proportionality, divide the value of one variable by the corresponding value of the other variable.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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