To find the slope of the red line that is perpendicular to the green line with a slope of \(-\frac{1}{4}\), we can use the property that the product of the slopes of two perpendicular lines is \(-1\).
Let \(m_1\) be the slope of the green line (which is \(-\frac{1}{4}\)) and \(m_2\) be the slope of the red line. The relationship can be expressed as:
\[ m_1 \times m_2 = -1 \]
Substituting the value of \(m_1\):
\[ -\frac{1}{4} \times m_2 = -1 \]
To find \(m_2\), we can multiply both sides of the equation by \(-4\):
\[ m_2 = -1 \times -4 \]
This simplifies to:
\[ m_2 = 4 \]
Therefore, the slope of the red line is \(4\).