Consider the line \( 5 x+3 y=-8 \). What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?

To find the slope of a line perpendicular to the line given by the equation \( 5x + 3y = -8 \), we first need to identify the slope of the original line. We can rewrite it in slope-intercept form (y = mx + b) by solving for y: \[ 3y = -5x - 8 \quad \Rightarrow \quad y = -\frac{5}{3}x - \frac{8}{3} \] The slope (m) of this line is \(-\frac{5}{3}\). The slope of a line perpendicular to this line is the negative reciprocal of \(-\frac{5}{3}\), which is \(\frac{3}{5}\). The slope of a line parallel to the original line is the same as the original line's slope. Therefore, the slope of a line parallel to \( 5x + 3y = -8 \) is also \(-\frac{5}{3}\).