If \[$ Y \$\] Varies Directly As \[$ X \$\], And \[$ Y \$\] Is 48 When \[$ X \$\] Is 6, Which Expression Can Be Used To Find The Value Of \[$ Y \$\] When \[$ X \$\] Is 2?A. \[$ Y = \frac{48}{6} \times
Understanding Direct Variation
Direct variation is a fundamental concept in mathematics that describes the relationship between two variables, where one variable is a constant multiple of the other. In other words, if { y $}$ varies directly as { x $}$, it means that { y $}$ is equal to a constant multiple of { x $}$. This relationship can be represented by the equation { y = kx $}$, where { k $}$ is the constant of variation.
Given Information
We are given that { y $}$ varies directly as { x $}$, and { y $}$ is 48 when { x $}$ is 6. This information can be used to find the constant of variation, { k $}$. To do this, we can substitute the given values into the equation { y = kx $}$ and solve for { k $}$.
Finding the Constant of Variation
Substituting { y = 48 $}$ and { x = 6 $}$ into the equation { y = kx $}$, we get:
To solve for { k $}$, we can divide both sides of the equation by 6:
Therefore, the constant of variation is { k = 8 $}$.
Finding the Value of { y $}$ When { x $}$ is 2
Now that we have found the constant of variation, we can use it to find the value of { y $}$ when { x $}$ is 2. We can substitute { x = 2 $}$ and { k = 8 $}$ into the equation { y = kx $}$:
Therefore, the value of { y $}$ when { x $}$ is 2 is 16.
Conclusion
In this article, we have discussed the concept of direct variation and its applications in mathematics. We have also used the given information to find the constant of variation and the value of { y $}$ when { x $}$ is 2. The expression that can be used to find the value of { y $}$ when { x $}$ is 2 is { y = 8x $}$.
Final Answer
The final answer is { y = 8x $}$.
Direct Variation Formula
The direct variation formula is { y = kx $}$, where { k $}$ is the constant of variation.
Finding the Constant of Variation
To find the constant of variation, we can substitute the given values into the equation { y = kx $}$ and solve for { k $}$.
Direct Variation Examples
- If { y $}$ varies directly as { x $}$, and { y $}$ is 24 when { x $}$ is 3, find the constant of variation.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 36 when { x $}$ is 4, find the constant of variation.
Direct Variation Applications
Direct variation has many applications in real-life situations, such as:
- The cost of goods sold varies directly with the quantity sold.
- The distance traveled varies directly with the speed of the vehicle.
- The amount of money earned varies directly with the number of hours worked.
Direct Variation Problems
- If { y $}$ varies directly as { x $}$, and { y $}$ is 48 when { x $}$ is 6, find the value of { y $}$ when { x $}$ is 2.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 72 when { x $}$ is 9, find the value of { y $}$ when { x $}$ is 3.
Direct Variation Exercises
- If { y $}$ varies directly as { x $}$, and { y $}$ is 24 when { x $}$ is 3, find the constant of variation.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 36 when { x $}$ is 4, find the constant of variation.
Direct Variation Solutions
- If { y $}$ varies directly as { x $}$, and { y $}$ is 48 when { x $}$ is 6, the constant of variation is 8.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 72 when { x $}$ is 9, the constant of variation is 8.
Direct Variation Theorems
- If { y $}$ varies directly as { x $}$, then { y = kx $}$.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Proofs
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation equation.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Corollaries
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation equation.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Conjectures
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation equation.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Theorems and Proofs
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation equation.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Corollaries and Conjectures
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation equation.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Examples and Exercises
- If { y $}$ varies directly as { x $}$, and { y $}$ is 24 when { x $}$ is 3, find the constant of variation.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 36 when { x $}$ is 4, find the constant of variation.
Direct Variation Solutions and Theorems
- If { y $}$ varies directly as { x $}$, and { y $}$ is 48 when { x $}$ is 6, the constant of variation is 8.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 72 when { x $}$ is 9, the constant of variation is 8.
Direct Variation Proofs and Corollaries
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation equation.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Conjectures and Theorems
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation equation.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Examples and Solutions
- If { y $}$ varies directly as { x $}$, and { y $}$ is 24 when { x $}$ is 3, find the constant of variation.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 36 when { x $}$ is 4, find the constant of variation.
Direct Variation Theorems and Proofs
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation
Direct Variation Q&A ======================
Q: What is direct variation?
A: Direct variation is a relationship between two variables, where one variable is a constant multiple of the other. It can be represented by the equation { y = kx $}$, where { k $}$ is the constant of variation.
Q: How do I find the constant of variation?
A: To find the constant of variation, you can substitute the given values into the equation { y = kx $}$ and solve for { k $}$.
Q: What is the formula for direct variation?
A: The formula for direct variation is { y = kx $}$, where { k $}$ is the constant of variation.
Q: How do I use direct variation to solve problems?
A: To use direct variation to solve problems, you can substitute the given values into the equation { y = kx $}$ and solve for the unknown variable.
Q: What are some examples of direct variation?
A: Some examples of direct variation include:
- The cost of goods sold varies directly with the quantity sold.
- The distance traveled varies directly with the speed of the vehicle.
- The amount of money earned varies directly with the number of hours worked.
Q: How do I determine if a relationship is a direct variation?
A: To determine if a relationship is a direct variation, you can check if the equation is in the form { y = kx $}$. If it is, then the relationship is a direct variation.
Q: What are some common mistakes to avoid when working with direct variation?
A: Some common mistakes to avoid when working with direct variation include:
- Not checking if the equation is in the form { y = kx $}$.
- Not substituting the given values into the equation.
- Not solving for the unknown variable.
Q: How do I graph a direct variation?
A: To graph a direct variation, you can use a coordinate plane and plot the points { (x, y) $}$ that satisfy the equation { y = kx $}$.
Q: What are some real-world applications of direct variation?
A: Some real-world applications of direct variation include:
- The cost of goods sold varies directly with the quantity sold.
- The distance traveled varies directly with the speed of the vehicle.
- The amount of money earned varies directly with the number of hours worked.
Q: How do I use direct variation to solve problems in real-world situations?
A: To use direct variation to solve problems in real-world situations, you can substitute the given values into the equation { y = kx $}$ and solve for the unknown variable.
Q: What are some common problems that can be solved using direct variation?
A: Some common problems that can be solved using direct variation include:
- Finding the cost of goods sold based on the quantity sold.
- Finding the distance traveled based on the speed of the vehicle.
- Finding the amount of money earned based on the number of hours worked.
Q: How do I determine if a problem can be solved using direct variation?
A: To determine if a problem can be solved using direct variation, you can check if the relationship between the variables is a direct variation.
Q: What are some tips for working with direct variation?
A: Some tips for working with direct variation include:
- Make sure the equation is in the form { y = kx $}$.
- Substitute the given values into the equation.
- Solve for the unknown variable.
Q: How do I use direct variation to solve problems in mathematics?
A: To use direct variation to solve problems in mathematics, you can substitute the given values into the equation { y = kx $}$ and solve for the unknown variable.
Q: What are some common mistakes to avoid when working with direct variation in mathematics?
A: Some common mistakes to avoid when working with direct variation in mathematics include:
- Not checking if the equation is in the form { y = kx $}$.
- Not substituting the given values into the equation.
- Not solving for the unknown variable.
Q: How do I graph a direct variation in mathematics?
A: To graph a direct variation in mathematics, you can use a coordinate plane and plot the points { (x, y) $}$ that satisfy the equation { y = kx $}$.
Q: What are some real-world applications of direct variation in mathematics?
A: Some real-world applications of direct variation in mathematics include:
- The cost of goods sold varies directly with the quantity sold.
- The distance traveled varies directly with the speed of the vehicle.
- The amount of money earned varies directly with the number of hours worked.
Q: How do I use direct variation to solve problems in real-world situations in mathematics?
A: To use direct variation to solve problems in real-world situations in mathematics, you can substitute the given values into the equation { y = kx $}$ and solve for the unknown variable.
Q: What are some common problems that can be solved using direct variation in mathematics?
A: Some common problems that can be solved using direct variation in mathematics include:
- Finding the cost of goods sold based on the quantity sold.
- Finding the distance traveled based on the speed of the vehicle.
- Finding the amount of money earned based on the number of hours worked.
Q: How do I determine if a problem can be solved using direct variation in mathematics?
A: To determine if a problem can be solved using direct variation in mathematics, you can check if the relationship between the variables is a direct variation.
Q: What are some tips for working with direct variation in mathematics?
A: Some tips for working with direct variation in mathematics include:
- Make sure the equation is in the form { y = kx $}$.
- Substitute the given values into the equation.
- Solve for the unknown variable.
Direct Variation Formula
The direct variation formula is { y = kx $}$, where { k $}$ is the constant of variation.
Finding the Constant of Variation
To find the constant of variation, you can substitute the given values into the equation { y = kx $}$ and solve for { k $}$.
Direct Variation Examples
- If { y $}$ varies directly as { x $}$, and { y $}$ is 24 when { x $}$ is 3, find the constant of variation.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 36 when { x $}$ is 4, find the constant of variation.
Direct Variation Applications
Direct variation has many applications in real-life situations, such as:
- The cost of goods sold varies directly with the quantity sold.
- The distance traveled varies directly with the speed of the vehicle.
- The amount of money earned varies directly with the number of hours worked.
Direct Variation Problems
- If { y $}$ varies directly as { x $}$, and { y $}$ is 48 when { x $}$ is 6, find the value of { y $}$ when { x $}$ is 2.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 72 when { x $}$ is 9, find the value of { y $}$ when { x $}$ is 3.
Direct Variation Exercises
- If { y $}$ varies directly as { x $}$, and { y $}$ is 24 when { x $}$ is 3, find the constant of variation.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 36 when { x $}$ is 4, find the constant of variation.
Direct Variation Solutions
- If { y $}$ varies directly as { x $}$, and { y $}$ is 48 when { x $}$ is 6, the constant of variation is 8.
- If { y $}$ varies directly as { x $}$, and { y $}$ is 72 when { x $}$ is 9, the constant of variation is 8.
Direct Variation Theorems
- If { y $}$ varies directly as { x $}$, then { y = kx $}$.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Proofs
- If { y $}$ varies directly as { x $}$, then { y = kx $}$ is a direct variation equation.
- If { y $}$ varies directly as { x $}$, then { k $}$ is a constant.
Direct Variation Corollaries
- If { y $}$ varies directly as { x $}