Final answer:
The equation in point-slope form for the line perpendicular to y = -4x - 1 that passes through (-2, 7) is y - 7 = (1/4)(x + 2).
Step-by-step explanation:
The equation of the line perpendicular to y = -4x - 1 in point-slope form can be determined by using the fact that the slopes of perpendicular lines are negative reciprocals. The given line has a slope of -4, so the perpendicular line will have a slope of 1/4.
Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Given that the line passes through the point (-2, 7), we can substitute these values into the equation to find the equation of the line perpendicular to y = -4x - 1.
Using the point-slope form, we get: y - 7 = 1/4(x - (-2))
Finally, simplifying this equation gives us the equation in point-slope form for the line perpendicular to y = -4x - 1 that passes through (-2, 7): y - 7 = (1/4)(x + 2).