Final answer:
The equation of the line passing through the origin and (-5, 6) is y = -6/5x.
Step-by-step explanation:
The equation of the line passing through the origin and (-5, 6) can be found using the slope-intercept form of a linear equation, which is y = mx + b.
The slope of the line can be calculated using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get: m = (6 - 0) / (-5 - 0) = -6/5.
Since the line passes through the origin, the y-intercept, b, is 0. Therefore, the equation of the line is y = -6/5x (Option D).