[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:y=\dfrac{1}{2}x-9\to m_1=\dfrac{1}{2}\\\\l:y=mx+b\to\dfrac{1}{2}m=-1\qquad|\cdot2\\\\m=-2\\\\l:y=-2x+b\\\\\text{Put the coordinates of the point (7, 10) to the equation of the line}\ l:\\\\10=-2(7)+b\\10=-14+b\qquad|+14\\b=24\\\\Answer:\ y=-2x+24[/tex]
