\(y_1=m_1 x + b_1\)
is perpendicular to
\(y_2=m_2 x + b_2\)
if \(m_1 m_2 = -1\)
(see https://www.mathsisfun.com/algebra/line-parallel-perpendicular.html for more information)
\(m_1 = 4 \\ m_2 = -1/4\)
Given that the line should passes through (8,1), we get \(b_2\):
\(1=-1/4*8+b_2 \\ b_2 = 3\)
So, the answer is: \(y=-1/4 x + 3\)
.