Mathematics Grade 7 5.1.5 Quiz: Proportional RelationshipsQuestion 2 Of 5The Equation $y=5x$ Represents A Proportional Relationship. What Is The Constant Of Proportionality?A. $\frac{1}{5}$ B. 5 C. \$x$[/tex\] D. 0
Introduction
In mathematics, proportional relationships are a fundamental concept that helps us understand how different quantities are related to each other. A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other. In this article, we will focus on the concept of proportional relationships and how to identify the constant of proportionality.
What is a Proportional Relationship?
A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other. This means that if we multiply one variable by a constant, we get the other variable. For example, if we have a relationship between the number of apples and the number of bananas, and we know that for every 2 apples, we get 3 bananas, then this is a proportional relationship.
The Equation of a Proportional Relationship
The equation of a proportional relationship is in the form of y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality. In the given equation y = 5x, we can see that the constant of proportionality is 5.
What is the Constant of Proportionality?
The constant of proportionality is a number that represents the ratio of the two variables in a proportional relationship. In the equation y = 5x, the constant of proportionality is 5, which means that for every 1 unit of x, we get 5 units of y.
How to Identify the Constant of Proportionality
To identify the constant of proportionality, we need to look at the equation of the proportional relationship. In the equation y = 5x, the constant of proportionality is 5, which is the number that is multiplied by x to get y.
Solving the Problem
Now, let's solve the problem given in the question. The equation y = 5x represents a proportional relationship. What is the constant of proportionality?
To solve this problem, we need to look at the equation and identify the constant of proportionality. In the equation y = 5x, the constant of proportionality is 5.
Conclusion
In conclusion, the constant of proportionality is a number that represents the ratio of the two variables in a proportional relationship. In the equation y = 5x, the constant of proportionality is 5. We can identify the constant of proportionality by looking at the equation of the proportional relationship.
Answer
The correct answer is B. 5.
Additional Examples
Here are some additional examples of proportional relationships:
- y = 2x
- y = 3x
- y = 4x
In each of these examples, the constant of proportionality is the number that is multiplied by x to get y.
Real-World Applications
Proportional relationships have many real-world applications. For example, if we know that a car travels 25 miles per gallon, then we can use this information to calculate how far the car will travel on a certain amount of gasoline.
Practice Problems
Here are some practice problems to help you understand proportional relationships:
- If y = 3x, what is the constant of proportionality?
- If y = 2x, what is the constant of proportionality?
- If y = 4x, what is the constant of proportionality?
Answer Key
Here is the answer key for the practice problems:
- The constant of proportionality is 3.
- The constant of proportionality is 2.
- The constant of proportionality is 4.
Conclusion
Frequently Asked Questions
Q: What is a proportional relationship?
A: A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other. This means that if we multiply one variable by a constant, we get the other variable.
Q: What is the equation of a proportional relationship?
A: The equation of a proportional relationship is in the form of y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.
Q: How do I identify the constant of proportionality?
A: To identify the constant of proportionality, we need to look at the equation of the proportional relationship. In the equation y = 5x, the constant of proportionality is 5, which is the number that is multiplied by x to get y.
Q: What is the constant of proportionality in the equation y = 2x?
A: The constant of proportionality in the equation y = 2x is 2.
Q: What is the constant of proportionality in the equation y = 3x?
A: The constant of proportionality in the equation y = 3x is 3.
Q: How do I use proportional relationships in real-world applications?
A: Proportional relationships have many real-world applications. For example, if we know that a car travels 25 miles per gallon, then we can use this information to calculate how far the car will travel on a certain amount of gasoline.
Q: What are some examples of proportional relationships?
A: Here are some examples of proportional relationships:
- y = 2x
- y = 3x
- y = 4x
Q: How do I solve problems involving proportional relationships?
A: To solve problems involving proportional relationships, we need to identify the constant of proportionality and use it to solve for the unknown variable.
Q: What is the constant of proportionality in the equation y = 5x?
A: The constant of proportionality in the equation y = 5x is 5.
Q: How do I determine if a relationship is proportional?
A: To determine if a relationship is proportional, we need to check if the ratio of the two variables is constant. If the ratio is constant, then the relationship is proportional.
Q: What are some common mistakes to avoid when working with proportional relationships?
A: Here are some common mistakes to avoid when working with proportional relationships:
- Not identifying the constant of proportionality correctly
- Not using the correct equation for the proportional relationship
- Not checking if the ratio of the two variables is constant
Conclusion
In conclusion, proportional relationships are an important concept in mathematics that helps us understand how different quantities are related to each other. By understanding proportional relationships, we can solve problems involving real-world applications and make informed decisions.