Final answer:
The slope of a line perpendicular to the line with equation y = 4x + ½ is -1/4, as perpendicular lines have slopes that are negative reciprocals.
Step-by-step explanation:
The equation of a line provided is y = 4x + ½. To find the slope of a line perpendicular to this line, we must be aware of the concept that perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is the coefficient of x, which is 4. Therefore, the slope of a line that is perpendicular to the given line would be the negative reciprocal of 4, which is -1/4. This means our perpendicular line will have a slope of -1/4.