Final answer:
To find a line perpendicular to y = 1/3x - 3 and containing the point (2, -6), we need to find the negative reciprocal of the slope of the given line and use the point-slope form to write the equation of the perpendicular line. The correct answer is option A, y = 3x - 12.
Step-by-step explanation:
To find a line that is perpendicular to y = 1/3x - 3 and contains the point (2, -6), we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line has a slope of 1/3, so the perpendicular line will have a slope of -3.
Using the point-slope form, we can write the equation of the perpendicular line as y - y1 = m(x - x1), where m = -3 and (x1, y1) = (2, -6).Plugging in the values, we get y - (-6) = -3(x - 2).
Simplifying the equation gives us y + 6 = -3x + 6. Rearranging the equation, we get y = -3x. The correct answer is option A, y = 3x - 12, since it represents the line y = -3x but with different y-intercept.