What is the equation of the line perpendicular to 2 x minus 3 y is equal to 13 that passes through the point open paren negative 6 comma 5 close paren ?

Rewrite 2x − 3y = 13 as y = (2/3)x − 13/3, so its slope is 2/3. A perpendicular line has slope −3/2, the negative reciprocal. Using the point (−6, 5), its equation is y − 5 = (−3/2)(x + 6), which simplifies to y = −(3/2)x − 4. Therefore, the answer is choice C, y = −(3/2)x − 4.

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