Final answer:
The equation of the line that is perpendicular to f(x) and passes through the point (4, -6) is 3x + 4y = -12.
Step-by-step explanation:
To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to determine the slope of the given line, and then find the negative reciprocal of that slope to get the slope of the perpendicular line.
Given that the point (4, -6) lies on the line, we can substitute the coordinates into the equation and solve for the y-intercept.
The equation of the line that is perpendicular to f(x) and passes through the point (4, -6) is 3x + 4y = -12 (option B).