To find the slope of a line that is perpendicular to the line given by the equation \( y = \frac{5}{8}x - 2 \), we first need to identify the slope of the original line.
In the equation \( y = \frac{5}{8}x - 2 \), the slope (\( m \)) is \( \frac{5}{8} \).
The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. To find the negative reciprocal of \( \frac{5}{8} \), we do the following:
- Flip the fraction: \( \frac{8}{5} \)
- Change the sign: \( -\frac{8}{5} \)
Therefore, the slope of a line perpendicular to the line \( y = \frac{5}{8}x - 2 \) is \( -\frac{8}{5} \).