Final answer:
The line perpendicular to y=4x+7 passing through (-8,2) has the equation in point-slope form as (y - 2) = -1/4(x + 8), which is option A.
Step-by-step explanation:
The question is asking for the equation of a line that is perpendicular to the given line y = 4x + 7 and passes through the point (-8,2). To find this, we must use the concept that perpendicular lines have slopes that are negative reciprocals of each other. Since the slope of the given line is 4, the slope of the line perpendicular to it will be -1/4. Using the point-slope form, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through, the equation can be written. Substituting the slope -1/4 and the point (-8,2) into the point-slope form, we get the equation (y - 2) = -1/4(x + 8), which matches option A.