Final answer:
The equation of the line parallel to AB and passing through the origin is 3x + 5y = 0.
Step-by-step explanation:
To find the equation of a line parallel to AB and passing through the origin, we first need to find the slope of AB. The formula to find the slope between two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1). So, the slope of AB is (5 - 0) / (-6 - (-3)) = 5 / -3.
Since the line we are looking for is parallel to AB, it will have the same slope. The equation of a line with slope m passing through the origin (0, 0) is y = mx. Therefore, the equation of the line that is parallel to AB and passes through the origin is 3x + 5y = 0.