To find the slope of a line that is perpendicular to the given line \( y = -\frac{4}{3}x + 2 \), we need to determine the negative reciprocal of the slope of the given line.
The slope of the given line is \( -\frac{4}{3} \).
The negative reciprocal of \( -\frac{4}{3} \) is calculated as follows:
- Take the reciprocal: The reciprocal of \( -\frac{4}{3} \) is \( -\frac{3}{4} \).
- Change the sign: The negative reciprocal is \( \frac{3}{4} \).
Thus, the slope \( m \) of a line perpendicular to the given line is:
\[ m = \frac{3}{4} \]