[tex]Let\ k:y=m_1x+b_1\ and\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\We\ have\ k:y=\dfrac{x}{4}+5=\dfrac{1}{4}x+5\to m_1=\dfrac{1}{4}.\\\\Let\ l:y=mx+b\\\\l\ \perp\ k\iff\dfrac{1}{4}m=-1\qquad|\cdot4\to m=-4\\\\l:y=-4x+b.\\\\The\ line\ l\ passes\ through\ the\ point\ (2,\ 7).\ Substitute\ the\ coordinates\\to\ the\ equation\ of\ the\ line\ l:\\\\7=-4(2)+b\\7=-8+b\qquad|+8\\15=b\to b=15\\\\Answer:\ \boxed{y=-4x+15}[/tex]
