Final answer:
The equation of a line perpendicular to y = -2/3x and passing through the point (6,-5) is y = 3/2x - 14, which corresponds to option A.
Step-by-step explanation:
The equation that represents a line perpendicular to the line y = -2/3x must have a slope that is the negative reciprocal of -2/3. The negative reciprocal of -2/3 is 3/2.
Therefore, we need to find an option with a slope of 3/2 that also passes through the point (6,-5). Using the slope-intercept form, y = mx + b, and the point (6,-5), we can substitute m with 3/2 and the coordinates of the point into the equation to find b:
y = (3/2)x + b
-5 = (3/2)(6) + b
-5 = 9 + b
b = -14
The correct equation is y = 3/2x - 14, which is option A.