Final answer:
The equation of a line perpendicular to 5x - 6y = -7 and passing through the point (-5, 4) is 6x + 5y = -29, which corresponds to option A.
Step-by-step explanation:
The question asks for the equation of a line perpendicular to the given line 5x - 6y = -7 and passing through the point (-5, 4). To find the slope of the given line, we need to rearrange it into slope-intercept form (y = mx + b), where m is the slope. The given equation can be rewritten as 6y = 5x + 7, then y = (5/6)x + 7/6. The slope of the given line is 5/6, hence the slope of the line perpendicular to it will be the negative reciprocal, which is -6/5.
Using the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point (-5, 4), and m is the perpendicular slope -6/5, we can substitute the values to get the equation of the perpendicular line: y - 4 = (-6/5)(x + 5). Simplifying the equation into the general form Ax + By = C, we get 6x + 5y = -29, which matches option A.