Final answer:
A line that is perpendicular to 8x = -1 has a slope of 8. The equation -x = 8 represents a line with a perpendicular slope of 8.
Step-by-step explanation:
A line that is perpendicular to the line of 8x = -1 will have a slope that is the negative reciprocal of the slope of the given line. The given line can be rewritten in slope-intercept form as y = -1/8x, so the slope of the given line is -1/8. The slope of a line perpendicular to this line will be the negative reciprocal of -1/8, which is 8.
The equation of a line with slope 8 can be written in the form y = 8x + b, where b is the y-intercept. Since no specific y-intercept is given, the equation of the line perpendicular to 8x = -1 is represented by the equation y = 8x + b, where b is a constant value.
Based on the given options, the correct equation that represents a line perpendicular to 8x = -1 is a) -x = 8, because it can be rearranged to the standard form y = 8x + b where b = 0.