Final answer:
The slope of a line perpendicular to 3x - 6y = -72 is 2.
Step-by-step explanation:
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The equation of the given line is 3x - 6y = -72. We can rearrange this equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
So, the slope of the given line is -1/2. Therefore, the slope of a line perpendicular to it will be the negative reciprocal of -1/2, which is 2.