Practice: Proportional Relationships - Level GThe Equation $y = 3.5x$ Represents The Relationship Between $x$, The Number Of Items, And $y$, The Price.Which Ordered Pairs Represent An Amount Of Items And The Corresponding

Understanding Proportional Relationships

Proportional relationships are a fundamental concept in mathematics that describe the relationship between two or more variables. In this article, we will focus on the equation $y = 3.5x$, which represents the relationship between the number of items, $x$, and the price, $y$. We will explore how to identify ordered pairs that represent an amount of items and the corresponding price.

What are Proportional Relationships?

A proportional relationship is a relationship between two or more variables where one variable is a constant multiple of the other variable. In other words, if we multiply one variable by a constant, we get the other variable. The equation $y = 3.5x$ is an example of a proportional relationship, where the price, $y$, is a constant multiple of the number of items, $x$.

Identifying Ordered Pairs

To identify ordered pairs that represent an amount of items and the corresponding price, we need to substitute different values of $x$ into the equation $y = 3.5x$ and calculate the corresponding value of $y$. Let's consider a few examples:

• If $x = 2$, then $y = 3.5(2) = 7$. Therefore, the ordered pair $(2, 7)$ represents an amount of items and the corresponding price.
• If $x = 5$, then $y = 3.5(5) = 17.5$. Therefore, the ordered pair $(5, 17.5)$ represents an amount of items and the corresponding price.
• If $x = 10$, then $y = 3.5(10) = 35$. Therefore, the ordered pair $(10, 35)$ represents an amount of items and the corresponding price.

Examples of Ordered Pairs

Let's consider a few more examples of ordered pairs that represent an amount of items and the corresponding price:

• $(1, 3.5)$
• $(4, 14)$
• $(8, 28)$
• $(12, 42)$

Tips for Identifying Ordered Pairs

To identify ordered pairs that represent an amount of items and the corresponding price, follow these tips:

• Substitute different values of $x$ into the equation $y = 3.5x$.
• Calculate the corresponding value of $y$.
• Write the ordered pair in the form $(x, y)$.

Practice Problems

Here are a few practice problems to help you identify ordered pairs that represent an amount of items and the corresponding price:

• If $x = 3$, what is the corresponding value of $y$?
• If $x = 6$, what is the corresponding value of $y$?
• If $x = 9$, what is the corresponding value of $y$?

Solutions

• If $x = 3$, then $y = 3.5(3) = 10.5$. Therefore, the ordered pair $(3, 10.5)$ represents an amount of items and the corresponding price.
• If $x = 6$, then $y = 3.5(6) = 21$. Therefore, the ordered pair $(6, 21)$ represents an amount of items and the corresponding price.
• If $x = 9$, then $y = 3.5(9) = 31.5$. Therefore, the ordered pair $(9, 31.5)$ represents an amount of items and the corresponding price.

Conclusion

In conclusion, proportional relationships are a fundamental concept in mathematics that describe the relationship between two or more variables. The equation $y = 3.5x$ represents the relationship between the number of items, $x$, and the price, $y$. By substituting different values of $x$ into the equation and calculating the corresponding value of $y$, we can identify ordered pairs that represent an amount of items and the corresponding price. With practice and patience, you can become proficient in identifying ordered pairs that represent proportional relationships.

Glossary

• Proportional relationship: A relationship between two or more variables where one variable is a constant multiple of the other variable.
• Ordered pair: A pair of values that represent an amount of items and the corresponding price.
• Constant multiple: A constant that is multiplied by a variable to get another variable.

References

• [1] Khan Academy. (n.d.). Proportional Relationships. Retrieved from https://www.khanacademy.org/math/algebra/x2f-proportional-and-linear-equations/x2f-proportional-equations/x2f-proportional-equations/v/proportional-equations
• [2] Math Open Reference. (n.d.). Proportional Relationships. Retrieved from https://www.mathopenref.com/proportional.html

Additional Resources

• Khan Academy: Proportional Relationships
• Math Open Reference: Proportional Relationships
• IXL: Proportional Relationships

Practice Problems

Here are a few practice problems to help you identify ordered pairs that represent an amount of items and the corresponding price:

• If $x = 1$, what is the corresponding value of $y$?
• If $x = 2$, what is the corresponding value of $y$?
• If $x = 3$, what is the corresponding value of $y$?

Solutions

• If $x = 1$, then $y = 3.5(1) = 3.5$. Therefore, the ordered pair $(1, 3.5)$ represents an amount of items and the corresponding price.
• If $x = 2$, then $y = 3.5(2) = 7$. Therefore, the ordered pair $(2, 7)$ represents an amount of items and the corresponding price.
• If $x = 3$, then $y = 3.5(3) = 10.5$. Therefore, the ordered pair $(3, 10.5)$ represents an amount of items and the corresponding price.

Conclusion

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Q&A: Proportional Relationships

Q: What is a proportional relationship?

A: A proportional relationship is a relationship between two or more variables where one variable is a constant multiple of the other variable.

Q: What is an example of a proportional relationship?

A: The equation $y = 3.5x$ is an example of a proportional relationship, where the price, $y$, is a constant multiple of the number of items, $x$.

Q: How do I identify ordered pairs that represent an amount of items and the corresponding price?

A: To identify ordered pairs that represent an amount of items and the corresponding price, substitute different values of $x$ into the equation $y = 3.5x$ and calculate the corresponding value of $y$.

Q: What is an ordered pair?

A: An ordered pair is a pair of values that represent an amount of items and the corresponding price.

Q: How do I write an ordered pair?

A: To write an ordered pair, use the form $(x, y)$, where $x$ is the number of items and $y$ is the price.

Q: What is a constant multiple?

A: A constant multiple is a constant that is multiplied by a variable to get another variable.

Q: How do I calculate the corresponding value of $y$?

A: To calculate the corresponding value of $y$, multiply the value of $x$ by the constant multiple, which is 3.5 in this case.

Q: What are some examples of ordered pairs that represent an amount of items and the corresponding price?

A: Some examples of ordered pairs that represent an amount of items and the corresponding price are:

• $(1, 3.5)$
• $(2, 7)$
• $(3, 10.5)$
• $(4, 14)$
• $(5, 17.5)$

Q: How do I practice identifying ordered pairs that represent an amount of items and the corresponding price?

A: To practice identifying ordered pairs that represent an amount of items and the corresponding price, try substituting different values of $x$ into the equation $y = 3.5x$ and calculating the corresponding value of $y$.

Q: What are some resources that can help me learn more about proportional relationships?

A: Some resources that can help you learn more about proportional relationships include:

• Khan Academy: Proportional Relationships
• Math Open Reference: Proportional Relationships
• IXL: Proportional Relationships

Conclusion

In conclusion, proportional relationships are a fundamental concept in mathematics that describe the relationship between two or more variables. The equation $y = 3.5x$ represents the relationship between the number of items, $x$, and the price, $y$. By substituting different values of $x$ into the equation and calculating the corresponding value of $y$, we can identify ordered pairs that represent an amount of items and the corresponding price. With practice and patience, you can become proficient in identifying ordered pairs that represent proportional relationships.

Glossary

• Proportional relationship: A relationship between two or more variables where one variable is a constant multiple of the other variable.
• Ordered pair: A pair of values that represent an amount of items and the corresponding price.
• Constant multiple: A constant that is multiplied by a variable to get another variable.

References

• [1] Khan Academy. (n.d.). Proportional Relationships. Retrieved from https://www.khanacademy.org/math/algebra/x2f-proportional-and-linear-equations/x2f-proportional-equations/x2f-proportional-equations/v/proportional-equations
• [2] Math Open Reference. (n.d.). Proportional Relationships. Retrieved from https://www.mathopenref.com/proportional.html

Additional Resources

• Khan Academy: Proportional Relationships
• Math Open Reference: Proportional Relationships
• IXL: Proportional Relationships