Final answer:
The line perpendicular to y = 4x + 2 that passes through (-8, 5) is y = (-1/4)x + 3 or option C.
Step-by-step explanation:
The equation of the line that is perpendicular to the line y = 4x + 2 and that passes through the point (-8, 5) can be found using the concept of slopes. Since the given line has a slope of 4, the perpendicular line will have a slope that is the negative reciprocal of 4, which is -1/4. Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we can substitute in our point to solve for b.
Starting with y = (-1/4)x + b and plugging in the point (-8, 5),
5 = (-1/4)(-8) + b
5 = 2 + b
b = 3
Thus, the equation of the perpendicular line is y = (-1/4)x + 3, which matches option C.