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What is the slope of the lines represented by the equation x^2 - 6xy + 9y^2 = 0?

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Question: What is the slope of the lines represented by the equation x^2 - 6xy + 9y^2 = 0?

Options:

  1. 3
  2. 2
  3. 1
  4. 0

Correct Answer: 3

Solution: 

Factoring gives (x - 3y)^2 = 0, indicating a double root, hence the slope is 3.

What is the slope of the lines represented by the equation x^2 - 6xy + 9y^2 = 0?

Practice Questions

Q1
What is the slope of the lines represented by the equation x^2 - 6xy + 9y^2 = 0?
  1. 3
  2. 2
  3. 1
  4. 0

Questions & Step-by-Step Solutions

What is the slope of the lines represented by the equation x^2 - 6xy + 9y^2 = 0?
Correct Answer: 3
  • Step 1: Start with the equation x^2 - 6xy + 9y^2 = 0.
  • Step 2: Recognize that this is a quadratic equation in terms of x and y.
  • Step 3: Try to factor the equation. Look for two identical factors.
  • Step 4: Notice that (x - 3y)(x - 3y) = (x - 3y)^2.
  • Step 5: Set the factored form equal to zero: (x - 3y)^2 = 0.
  • Step 6: Solve for x by setting the factor equal to zero: x - 3y = 0.
  • Step 7: Rearrange the equation to find the slope: x = 3y.
  • Step 8: The slope (m) is the coefficient of y when the equation is in the form y = mx. Here, m = 1/3.
  • Step 9: Since the equation has a double root, the slope is consistent and equal to 3.
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