Final answer:
The point-slope form of the line perpendicular to a line with a slope of 1/4 and passing through (5, 5) is y - 5 = -4(x - 5).
Step-by-step explanation:
To write the point-slope form of a line that is perpendicular to another line, we need to find the perpendicular slope. Since the given slope of the original line is 1/4, the perpendicular slope is the negative reciprocal of 1/4, which is -4 (since the product of the slopes of two perpendicular lines in a plane is -1).
Next, we use the point-slope form, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the slope -4 and the point (5, 5), we get:
y - 5 = -4(x - 5)
This is the equation of the line in point-slope form.