Final answer:
The equation of the line that is perpendicular to the given line and passes through the point (2, -1) is y = -1/3x - 1/3, which is option (a).
Step-by-step explanation:
The question involves finding the equation of a perpendicular line in slope-intercept form that passes through a given point. Since the original line has a slope of 3, as per the slope-intercept form equation y = mx + b, where m is the slope, the perpendicular line will have a negative reciprocal slope, which is -1/3. Using the point (2, -1) to solve for the y-intercept, we calculate:
y = mx + b
-1 = (-1/3)(2) + b
-1 = -2/3 + b
b = -1 + 2/3
b = -3/3 + 2/3
b = -1/3
So the equation in slope-intercept form is y = -1/3x - 1/3, which corresponds to option (a).