To find the slope of a line that is perpendicular to a given line, you need to take the negative reciprocal of the slope of the original line.
The given line is in slope-intercept form \(y = mx + b\), where \(m\) is the slope. For the line \(y = \frac{2}{5}x + 4\), the slope \(m\) is \(\frac{2}{5}\).
To find the slope of the line that is perpendicular to it, we take the negative reciprocal of \(\frac{2}{5}\):
\[ m_{\perp} = -\frac{1}{\left(\frac{2}{5}\right)} = -\frac{5}{2} \]
Therefore, the slope of the line that is perpendicular to the original line is \(-\frac{5}{2}\).
So the answer is: • \(m_{\perp} = -\frac{5}{2}\)