Drag Numbers To The Table So It Shows A Proportional Relationship Between $x$ And $y$.${ \begin{tabular}{|c|c|} \hline X X X & Y Y Y \ \hline 0.8 & \ \hline \end{tabular} }$Available Numbers: 6.4, 64, 12.8, 5.6, 16,
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Understanding Proportional Relationships
In mathematics, a proportional relationship is a relationship between two variables, x and y, where the ratio of y to x is constant. This means that as x increases or decreases, y increases or decreases at a constant rate. In this article, we will explore how to establish a proportional relationship between two variables using a table.
Given Information
We are given a table with one row and two columns, x and y. The value of x is 0.8, and we need to find the corresponding value of y. We also have a set of available numbers: 6.4, 64, 12.8, 5.6, and 16.
The Goal
Our goal is to drag the available numbers to the table so that it shows a proportional relationship between x and y.
Step 1: Understand the Concept of Proportionality
To establish a proportional relationship, we need to understand that the ratio of y to x is constant. This means that if we multiply x by a certain factor, y should also be multiplied by the same factor.
Step 2: Analyze the Available Numbers
Let's analyze the available numbers: 6.4, 64, 12.8, 5.6, and 16. We need to find a number that is proportional to 0.8. To do this, we can try multiplying 0.8 by different factors to see if we get any of the available numbers.
Step 3: Find the Proportional Relationship
Let's try multiplying 0.8 by 8 to see if we get 6.4. We can write this as:
This shows that 6.4 is proportional to 0.8, since the ratio of 6.4 to 0.8 is 8.
Step 4: Verify the Proportional Relationship
To verify that 6.4 is proportional to 0.8, we can check if the ratio of 6.4 to 0.8 is constant. We can write this as:
This shows that the ratio of 6.4 to 0.8 is indeed 8, which means that 6.4 is proportional to 0.8.
Step 5: Fill in the Table
Now that we have found the proportional relationship, we can fill in the table with the corresponding value of y. We can write this as:
\begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 0.8 & 6.4 \\ \hline \end{tabular}
Conclusion
In this article, we have established a proportional relationship between x and y using a table. We have analyzed the available numbers and found that 6.4 is proportional to 0.8. We have verified this relationship by checking if the ratio of 6.4 to 0.8 is constant. Finally, we have filled in the table with the corresponding value of y.
Tips and Variations
- To establish a proportional relationship between two variables, you can use the following formula:
where k is the constant of proportionality.
- To find the constant of proportionality, you can use the following formula:
- To verify a proportional relationship, you can check if the ratio of y to x is constant.
Practice Problems
- Find the proportional relationship between x and y using the following table:
\begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 2 & \\ \hline \end{tabular}
Available numbers: 16, 32, 64, 128, 256
- Find the proportional relationship between x and y using the following table:
\begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 0.5 & \\ \hline \end{tabular}
Available numbers: 2, 4, 8, 16, 32
Solutions
- The proportional relationship between x and y is:
The corresponding value of y is 128.
- The proportional relationship between x and y is:
The corresponding value of y is 4.
Conclusion
In this article, we have established a proportional relationship between x and y using a table. We have analyzed the available numbers and found the corresponding value of y. We have verified this relationship by checking if the ratio of y to x is constant. Finally, we have filled in the table with the corresponding value of y.
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Frequently Asked Questions
Q: What is a proportional relationship?
A: A proportional relationship is a relationship between two variables, x and y, where the ratio of y to x is constant. This means that as x increases or decreases, y increases or decreases at a constant rate.
Q: How do I establish a proportional relationship between two variables?
A: To establish a proportional relationship, you can use the following formula:
where k is the constant of proportionality. You can find the constant of proportionality by using the following formula:
Q: How do I verify a proportional relationship?
A: To verify a proportional relationship, you can check if the ratio of y to x is constant. You can do this by dividing y by x and checking if the result is the same for different values of x.
Q: What is the constant of proportionality?
A: The constant of proportionality is a number that represents the ratio of y to x in a proportional relationship. It is denoted by the letter k and is calculated using the formula:
Q: How do I find the constant of proportionality?
A: To find the constant of proportionality, you can use the following formula:
You can plug in the values of y and x to find the constant of proportionality.
Q: What is the difference between a proportional relationship and a linear relationship?
A: A proportional relationship is a relationship between two variables where the ratio of y to x is constant. A linear relationship is a relationship between two variables where the graph of the relationship is a straight line. While all proportional relationships are linear, not all linear relationships are proportional.
Q: Can a proportional relationship have a negative constant of proportionality?
A: Yes, a proportional relationship can have a negative constant of proportionality. This means that as x increases, y decreases, and vice versa.
Q: Can a proportional relationship have a zero constant of proportionality?
A: No, a proportional relationship cannot have a zero constant of proportionality. This is because a zero constant of proportionality would mean that y is equal to zero for all values of x, which is not a proportional relationship.
Q: Can a proportional relationship have a fractional constant of proportionality?
A: Yes, a proportional relationship can have a fractional constant of proportionality. This means that the ratio of y to x is a fraction, such as 1/2 or 3/4.
Q: Can a proportional relationship have a decimal constant of proportionality?
A: Yes, a proportional relationship can have a decimal constant of proportionality. This means that the ratio of y to x is a decimal, such as 0.5 or 2.5.
Q: Can a proportional relationship have a negative decimal constant of proportionality?
A: Yes, a proportional relationship can have a negative decimal constant of proportionality. This means that as x increases, y decreases, and vice versa.
Q: Can a proportional relationship have a fractional decimal constant of proportionality?
A: Yes, a proportional relationship can have a fractional decimal constant of proportionality. This means that the ratio of y to x is a fraction of a decimal, such as 0.25 or 0.75.
Q: Can a proportional relationship have a negative fractional decimal constant of proportionality?
A: Yes, a proportional relationship can have a negative fractional decimal constant of proportionality. This means that as x increases, y decreases, and vice versa.
Conclusion
In this article, we have answered some of the most frequently asked questions about proportional relationships. We have covered topics such as establishing a proportional relationship, verifying a proportional relationship, and finding the constant of proportionality. We have also discussed some of the properties of proportional relationships, such as the constant of proportionality and the ratio of y to x.