Final answer:
The equation of the line passing through the point (4, -5) and perpendicular to the line x + 2y = 5 is 2x - y = 13, which corresponds to option D.
Step-by-step explanation:
The equation that represents the line passing through the point (4, -5) and perpendicular to the line x + 2y = 5 can be found by first determining the slope of the given line. The slope of the line x + 2y = 5 is -0.5, since if we rewrite it in slope-intercept form (y = mx + b), we would have y = -0.5x + 2.5.
A line perpendicular to this one would have a slope that is the negative reciprocal of -0.5, which is 2. Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point (4, -5), we substitute m with 2 and simplify to get the equation of the line in standard form. Doing this, we find the equation is 2x - y = 13, which is option D.