What is the equation of the line perpendicular to y is equal to 2 thirds x plus 1 that passes through the point open paren 12 comma negative 6 close paren ?

The given line has slope 2/3, so a perpendicular line has slope −3/2, the negative reciprocal. Using the point (12, −6), the point-slope equation is y + 6 = −(3/2)(x − 12). Simplifying gives 3x + 2y = 24, which is choice A, “3x plus 2y is equal to 24.”

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