Final answer:
The slope of a perpendicular line is the negative reciprocal of the given line's slope. Given the equation 3x + y = -4, the slope of the original line is -3, and thus the slope of a perpendicular line is 1/3, answer d).
Step-by-step explanation:
The question asks for the slope of a line perpendicular to the given line with the equation 3x + y = -4. To solve this, we first need to find the slope of the given line by rearranging it into slope-intercept form, y = mx + b, where m represents the slope. By doing so we get the equation to the form y = -3x - 4, which reveals that the slope of the given line is -3. The slope of a line perpendicular to this one would be the negative reciprocal of -3, which is 1/3. Thus, the correct answer is d) 1/3.