Final answer:
The correct slope of a line perpendicular to the line given by the equation 3x - 6y = -72 is -2, since the original line's slope is 1/2 and perpendicular slopes are negative reciprocals.
Step-by-step explanation:
To find the slope of a line which is perpendicular to the line given by the equation 3x - 6y = -72, we first need to write the equation in slope-intercept form, which is y = mx + b. Here, m represents the slope and b represents the y-intercept. We can solve for y to get the slope-intercept form:
- 3x - 6y = -72
- 6y = 3x + 72
- y = (1/2)x + 12
The slope m of this line is 1/2. The slope of a line perpendicular to this one will be the negative reciprocal of 1/2, which is -2. Therefore, the correct answer is B. 2/3.