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Is 3x - 4y = 12 parallel or perpendicular

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Final answer:

The equation 3x - 4y = 12 is neither parallel nor perpendicular to any specific line.

Step-by-step explanation:

A linear equation in the form ax + by = c is parallel to another linear equation in the form ex + fy = g if and only if the ratios of their coefficients are equal and not both zero. In this case, the equation 3x - 4y = 12 is parallel to another equation if the ratio of the coefficients of x and y is the same. Since the coefficient of x is 3 and the coefficient of y is -4, the ratio is -3/4. Therefore, the equation is not parallel to the x-axis and not perpendicular to the y-axis, making it neither parallel nor perpendicular to any specific line.

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