Final answer:
The slope of a line that is perpendicular to the line represented by the equation -3y = 8x + 6 is 3/8, which is the negative reciprocal of the original line's slope.
Step-by-step explanation:
To find the slope of a line perpendicular to another line, we first need to find the slope of the given line. The equation -3y = 8x + 6 can be rewritten in the slope-intercept form (y = mx + b) by dividing all terms by -3, resulting in y = -8/3x - 2. The slope (m) of this line is -8/3. The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the slope of the line perpendicular to the given line is 3/8.