Final answer:
The correct answer is option D, y = 1/2x + 9. This is found by calculating the negative reciprocal of the slope of the original line and using the point-slope formula to find the new line's y-intercept.
Step-by-step explanation:
The correct answer is option D, which is y = ½x + 9. To find the equation of a line perpendicular to y = -2x that passes through a given point, you must first determine the slope of the original line. For the line y = -2x, the slope is -2. The slope of the line perpendicular to it will be the negative reciprocal of -2, which is ½. Now, using the slope-intercept form of a line (y = mx + b) where m is the slope and b is the y-intercept, we substitute the slope (½) and the given point (-3, 6) to solve for b:
y = mx + b
6 = (½)(-3) + b
6 = -³2 + b
6 + ³2 = b
b = 6 + ³2
b = 9
Therefore, the equation of the line is y = ½x + 9. This gives us the equation in option D.