[tex]Let\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\\text{We have}\ k:2y+4x=12\qquad|-4x\\\\2y=-4x+12\qquad|:2\\\\y=-2x+6\to m_1=-2\\\\l:y=mx+b\to-2m=-1\qquad|:(-2)\\\\m=\dfrac{1}{2}\\\\l:y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the point (8, 1) to the equation of the line}\ l:\\\\1=\dfrac{1}{2}(8)+b\\\\1=4+b\qquad|-4\\\\b=-3\\\\Answer:\ y=\dfrac{1}{2}x-3[/tex]
