Final answer:
The question seeks an equation of a line perpendicular to y = -2 passing through (4, -2). The correct equation should be x = 4, which is absent from the choices, indicating a potential mistake in the question options.
Step-by-step explanation:
The line that is perpendicular to y = -2 is a vertical line, because y = -2 is a horizontal line. Therefore, the slope of the perpendicular line must be undefined. This means that the perpendicular line has the form x = a, where a is a constant. Since the line must pass through the point (4, -2), the equation of the line is simply x = 4. However, none of the given options (A, B, C, or D) represent a vertical line. All the options given are equations of non-vertical lines, which means none of them are correct.