Final answer:
The correct equation of the line perpendicular to the given slope and passing through point A(5,3) is not among the options. In standard form, it should be -x + 2y = 1, but reversing signs for comparison to listed options gives x - 2y = -1, which is closest to option d, although not correct.
Step-by-step explanation:
The student wishes to find the equation of a line that is perpendicular to another line with a given slope and that passes through a specific point. Since the known line has a slope of -2, the slope of the line perpendicular to it will be its negative reciprocal, which is ½. Using the point (5, 3), we can apply the point-slope formula to find the equation of the new line, which then can be transformed into standard form. The equation in point-slope form is y - 3 = ½(x - 5). Converting this into standard form (Ax + By = C), we multiply everything by 2 to clear fractions, resulting in 2y - 6 = x - 5, and then we move all terms to one side: x - 2y = 5 - 6 which simplifies to x - 2y = -1. To match the options provided, we overturn the signs, getting -x + 2y = 1. However, as none of the provided options exactly match this equation, the original question may contain a typo. Assuming the student seeks the closest matching option, option d. x - 2y = 11 is the one that is closest in form, but it does not match the point (5, 3). The correct answer is not listed among the options given.