Finding the Expression for y

Oct 13, 2025 by windailys.com 120 views

Understanding Direct Variation

Direct variation is a type of relationship between two variables, where one variable is a constant multiple of the other. In other words, as one variable increases or decreases, the other variable increases or decreases at a constant rate. This relationship can be represented by the equation y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation.

Given Information

We are given that y varies directly as x, and y is 18 when x is 5. This means that we can use the equation y = kx to represent the relationship between y and x. We can also use the given information to find the value of k.

Finding the Value of k

To find the value of k, we can substitute the given values of y and x into the equation y = kx. This gives us:

18 = k(5)

To solve for k, we can divide both sides of the equation by 5:

k = 18/5

Finding the Expression for y

Now that we have found the value of k, we can use it to find the expression for y. We can substitute the value of k into the equation y = kx:

y = (18/5)x

Simplifying the Expression

We can simplify the expression for y by multiplying both sides of the equation by 5:

y = 18x/5

Finding the Value of y When x is 11

Now that we have the expression for y, we can use it to find the value of y when x is 11. We can substitute x = 11 into the equation:

y = 18(11)/5

To simplify the expression, we can multiply 18 and 11:

y = 198/5

Conclusion

In this article, we have discussed direct variation and its applications. We have used the given information to find the value of k and the expression for y. We have also used the expression for y to find the value of y when x is 11.

Answer

The correct expression for y is:

y = 18x/5

This expression can be used to find the value of y when x is 11.

Comparison of Options

Let's compare the given options with the correct expression:

A. y = (5/18)(11)

This expression is incorrect because it has the wrong value for k.

B. y = (18/5)(11)

This expression is incorrect because it has the wrong value for x.

Final Answer

The correct expression for y is:

y = 18x/5

This expression can be used to find the value of y when x is 11.

Direct Variation and Its Applications

Understanding Direct Variation

Given Information

Finding the Value of k

To find the value of k, we can substitute the given values of y and x into the equation y = kx. This gives us:

18 = k(5)

To solve for k, we can divide both sides of the equation by 5:

k = 18/5

Finding the Expression for y

Now that we have found the value of k, we can use it to find the expression for y. We can substitute the value of k into the equation y = kx:

y = (18/5)x

Simplifying the Expression

We can simplify the expression for y by multiplying both sides of the equation by 5:

y = 18x/5

Finding the Value of y When x is 11

Now that we have the expression for y, we can use it to find the value of y when x is 11. We can substitute x = 11 into the equation:

y = 18(11)/5

To simplify the expression, we can multiply 18 and 11:

y = 198/5

Conclusion

Answer

The correct expression for y is:

y = 18x/5

This expression can be used to find the value of y when x is 11.

Comparison of Options

Let's compare the given options with the correct expression:

A. y = (5/18)(11)

This expression is incorrect because it has the wrong value for k.

B. y = (18/5)(11)

This expression is incorrect because it has the wrong value for x.

Final Answer

The correct expression for y is:

y = 18x/5

Q: What is direct variation?

A: Direct variation is a type of relationship between two variables, where one variable is a constant multiple of the other. In other words, as one variable increases or decreases, the other variable increases or decreases at a constant rate.

Q: How is direct variation represented mathematically?

A: Direct variation is represented mathematically by the equation y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation.

Q: What is the constant of variation (k)?

A: The constant of variation (k) is a number that represents the constant rate at which the dependent variable (y) changes in response to changes in the independent variable (x).

Q: How do I find the value of k?

A: To find the value of k, you can use the given information to substitute the values of y and x into the equation y = kx. Then, you can solve for k by dividing both sides of the equation by x.

Q: What is the relationship between k and the given information?

A: The value of k is related to the given information by the equation k = y/x. This means that k is equal to the ratio of y to x.

Q: How do I use the value of k to find the expression for y?

A: To use the value of k to find the expression for y, you can substitute the value of k into the equation y = kx. This will give you the expression for y in terms of x.

Q: Can I simplify the expression for y?

A: Yes, you can simplify the expression for y by multiplying both sides of the equation by x. This will give you the expression for y in a simpler form.

Q: How do I use the expression for y to find the value of y when x is a specific value?

A: To use the expression for y to find the value of y when x is a specific value, you can substitute the value of x into the expression for y. This will give you the value of y.

Q: What if I have multiple values of x and y?

A: If you have multiple values of x and y, you can use the expression for y to find the value of y for each value of x. This will give you a table of values for y in terms of x.

Q: Can I use direct variation to model real-world situations?

A: Yes, direct variation can be used to model real-world situations where one variable is a constant multiple of another variable. Examples include the relationship between the distance traveled and the time taken, the relationship between the cost and the quantity of a product, and the relationship between the temperature and the pressure of a gas.

Q: What are some common applications of direct variation?

A: Some common applications of direct variation include:

Modeling the relationship between the distance traveled and the time taken
Modeling the relationship between the cost and the quantity of a product
Modeling the relationship between the temperature and the pressure of a gas
Modeling the relationship between the amount of substance and the concentration of a solution

Direct Variation Q&A

Q: What is direct variation?

Q: How is direct variation represented mathematically?

A: Direct variation is represented mathematically by the equation y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation.

Q: What is the constant of variation (k)?

A: The constant of variation (k) is a number that represents the constant rate at which the dependent variable (y) changes in response to changes in the independent variable (x).

Q: How do I find the value of k?

A: To find the value of k, you can use the given information to substitute the values of y and x into the equation y = kx. Then, you can solve for k by dividing both sides of the equation by x.

Q: What is the relationship between k and the given information?

A: The value of k is related to the given information by the equation k = y/x. This means that k is equal to the ratio of y to x.

Q: How do I use the value of k to find the expression for y?

A: To use the value of k to find the expression for y, you can substitute the value of k into the equation y = kx. This will give you the expression for y in terms of x.

Q: Can I simplify the expression for y?

A: Yes, you can simplify the expression for y by multiplying both sides of the equation by x. This will give you the expression for y in a simpler form.

Q: How do I use the expression for y to find the value of y when x is a specific value?

A: To use the expression for y to find the value of y when x is a specific value, you can substitute the value of x into the expression for y. This will give you the value of y.

Q: What if I have multiple values of x and y?

A: If you have multiple values of x and y, you can use the expression for y to find the value of y for each value of x. This will give you a table of values for y in terms of x.

Q: Can I use direct variation to model real-world situations?

Q: What are some common applications of direct variation?

A: Some common applications of direct variation include:

Modeling the relationship between the distance traveled and the time taken
Modeling the relationship between the cost and the quantity of a product
Modeling the relationship between the temperature and the pressure of a gas
Modeling the relationship between the amount of substance and the concentration of a solution