Find the slope of a line perpendicular to the line whose equation is \( 3 x-5 y=45 \). simplify your answer.

To find the slope of the line perpendicular to the given line, we first need to determine the slope of the line represented by the equation \( 3x - 5y = 45 \). We can rewrite this equation in slope-intercept form \( y = mx + b \). First, we isolate \( y \): \[ -5y = -3x + 45 \] Now, divide by -5: \[ y = \frac{3}{5}x - 9 \] The slope (m) of the original line is \( \frac{3}{5} \). The slope of the line that is perpendicular to this line is the negative reciprocal of \( \frac{3}{5} \). So, the slope of the perpendicular line is: \[ -\frac{1}{\left(\frac{3}{5}\right)} = -\frac{5}{3} \] Therefore, the slope of the line perpendicular to the given line is \( -\frac{5}{3} \).