What is the slope of the lines represented by the equation 5x^2 - 10xy + 5y^2 =

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Question: What is the slope of the lines represented by the equation 5x^2 - 10xy + 5y^2 = 0?

Options:

Correct Answer: 1

Solution:

The equation can be factored to find the slopes, which are both 1.

What is the slope of the lines represented by the equation 5x^2 - 10xy + 5y^2 = 0?

What is the slope of the lines represented by the equation 5x^2 - 10xy + 5y^2 = 0?

Step 1: Start with the equation 5x^2 - 10xy + 5y^2 = 0.
Step 2: Factor the equation. Notice that all terms have a common factor of 5, so we can divide the entire equation by 5.
Step 3: This simplifies the equation to x^2 - 2xy + y^2 = 0.
Step 4: Now, we can factor this quadratic expression. It can be factored as (x - y)(x - y) = 0, or (x - y)^2 = 0.
Step 5: Set each factor equal to zero. Since we have (x - y)^2 = 0, we get x - y = 0.
Step 6: Solve for y in terms of x. This gives us y = x.
Step 7: The slope of the line represented by y = x is 1.

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