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} \cdot

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Understanding Direct Variation

Direct variation is a relationship between two variables, x and y, where the value of y is directly proportional to the value of x. This means that as x increases, y also increases, and the relationship can be represented by the equation y = kx, where k is the constant of proportionality.

Given Information

We are given that y varies directly as x, and when x is 6, y is 48. We can use this information to find the constant of proportionality, k.

Finding the Constant of Proportionality

To find the constant of proportionality, k, we can use the given information: y = 48 when x = 6. We can substitute these values into the equation y = kx and solve for k.

48 = k(6)

To solve for k, we can divide both sides of the equation by 6:

k = 48/6
k = 8

Expression to Find the Value of y When x is 2

Now that we have found the constant of proportionality, k, 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:

y = 8(2)
y = 16

Therefore, the expression that can be used to find the value of y when x is 2 is y = 8x.

Alternative Expression

Another way to find the value of y when x is 2 is to use the given information: y = 48 when x = 6. We can set up a proportion to relate the two values:

48/6 = y/2

To solve for y, we can cross-multiply:

48(2) = 6y
96 = 6y

Now, we can divide both sides of the equation by 6 to solve for y:

y = 96/6
y = 16

Therefore, the expression that can be used to find the value of y when x is 2 is also y = 8x.

Conclusion

In this article, we have discussed direct variation and how to find the value of y when x is 2. We have used the given information to find the constant of proportionality, k, and then used it to find the value of y when x is 2. We have also shown that an alternative expression can be used to find the value of y when x is 2.

Key Takeaways

  • Direct variation is a relationship between two variables, x and y, where the value of y is directly proportional to the value of x.
  • The equation y = kx represents direct variation, where k is the constant of proportionality.
  • To find the value of y when x is 2, we can use the given information to find the constant of proportionality, k, and then substitute x = 2 and k = 8 into the equation y = kx.
  • An alternative expression can be used to find the value of y when x is 2 by setting up a proportion and solving for y.

Final Answer

Q: What is direct variation?

A: Direct variation is a relationship between two variables, x and y, where the value of y is directly proportional to the value of x. This means that as x increases, y also increases, and the relationship can be represented by the equation y = kx, where k is the constant of proportionality.

Q: How do I know if two variables are in direct variation?

A: To determine if two variables are in direct variation, you can use the following steps:

  1. Plot the data points on a graph.
  2. Check if the data points form a straight line.
  3. If the data points form a straight line, then the variables are in direct variation.

Q: What is the constant of proportionality?

A: The constant of proportionality, k, is a value that represents the ratio of y to x in a direct variation relationship. It is a constant value that does not change, regardless of the values of x and y.

Q: How do I find the constant of proportionality?

A: To find the constant of proportionality, k, you can use the following steps:

  1. Write the equation of direct variation: y = kx.
  2. Use the given information to substitute values for x and y into the equation.
  3. Solve for k by dividing both sides of the equation by x.

Q: What is the equation of direct variation?

A: The equation of direct variation is y = kx, where k is the constant of proportionality.

Q: Can I use a proportion to find the value of y when x is 2?

A: Yes, you can use a proportion to find the value of y when x is 2. To do this, you can set up a proportion using the given information and then solve for y.

Q: How do I set up a proportion to find the value of y when x is 2?

A: To set up a proportion, you can use the following steps:

  1. Write the equation of direct variation: y = kx.
  2. Use the given information to substitute values for x and y into the equation.
  3. Set up a proportion using the given information and the equation of direct variation.
  4. Solve for y by cross-multiplying and then dividing both sides of the equation by the value of x.

Q: Can I use a graph to find the value of y when x is 2?

A: Yes, you can use a graph to find the value of y when x is 2. To do this, you can plot the data points on a graph and then use the graph to find the value of y when x is 2.

Q: How do I use a graph to find the value of y when x is 2?

A: To use a graph to find the value of y when x is 2, you can follow these steps:

  1. Plot the data points on a graph.
  2. Draw a line through the data points to represent the direct variation relationship.
  3. Use the graph to find the value of y when x is 2 by reading the value of y from the graph.

Q: What are some real-world applications of direct variation?

A: Direct variation has many real-world applications, including:

  • Physics: The relationship between distance and time in a constant-speed motion is an example of direct variation.
  • Engineering: The relationship between the force applied to an object and the distance it travels is an example of direct variation.
  • Economics: The relationship between the price of a product and the quantity demanded is an example of direct variation.

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

A: Yes, you can use direct variation to model real-world data. To do this, you can follow these steps:

  1. Collect data on the variables of interest.
  2. Plot the data points on a graph.
  3. Check if the data points form a straight line.
  4. If the data points form a straight line, then you can use direct variation to model the data.

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 data points form a straight line before using direct variation.
  • Not using the correct equation of direct variation.
  • Not solving for the constant of proportionality correctly.
  • Not using the correct values for x and y in the equation of direct variation.