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

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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