[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have}\ k:y=2x+5\to m_1=2.\\\\l:y=mx+b\to m=-\dfrac{1}{2}\to y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through the point (-2, -4).}\ \text{Put the coordinates to the equation:}\\\\-4=-\dfrac{1}{2}(-2)+b\\\\-4=1+b\qquad\text{subtract 1 from both sides}\\\\-5=b\to b=-5\\\\Answer:\ \boxed{y=-\dfrac{1}{2}x-5}[/tex]
