For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum

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Question: For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum of the slopes?

Options:

Correct Answer: -5/6

Solution:

The sum of the slopes of the lines is given by -b/a, which is -5/6.

For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum of the slopes?

For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum of the slopes?

Step 1: Identify the given equation, which is 6x^2 + 5xy + y^2 = 0.
Step 2: Recognize that this is a quadratic equation in two variables (x and y).
Step 3: Rewrite the equation in the standard form of a conic section, which is Ax^2 + Bxy + Cy^2 = 0.
Step 4: Identify the coefficients: A = 6, B = 5, C = 1.
Step 5: Use the formula for the sum of the slopes of the lines represented by the equation, which is -B/A.
Step 6: Substitute the values of B and A into the formula: -5/6.
Step 7: Conclude that the sum of the slopes of the lines is -5/6.

Quadratic Equations – Understanding how to interpret and manipulate quadratic equations to find slopes of lines.
Slope of Lines – Using the relationship between coefficients in a quadratic equation to determine the slopes of the lines represented.
Sum of Slopes – Applying the formula for the sum of the slopes of the lines derived from a quadratic equation.