Final answer:
The slope of the line perpendicular to 5x - 3y = 9 is found by taking the negative reciprocal of the original line's slope. The original line has a slope of 5/3, therefore, the perpendicular slope is -3/5, which is option C.
Step-by-step explanation:
The slope of the line represented by the equation 5x - 3y = 9 is found by first rewriting the equation in slope-intercept form which is y = mx+b, where m is the slope and b is the y-intercept. Solving for y, we get the equation y = \frac{5}{3}x - 3, which reveals that the slope of the original line is \frac{5}{3}.
To find the slope of a line perpendicular to the original line, we need to take the negative reciprocal of the original line's slope. The negative reciprocal of \frac{5}{3} is -\frac{3}{5}. Therefore, the slope of a line perpendicular to the given line is -\frac{3}{5}, which corresponds to option C.