[tex]\text{Let}\ k:y=m_1x+b_!\ \text{and}\ y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have}\ y=\dfrac{9}{11}-\dfrac{5}{4}x\to m_1=-\dfrac{5}{4}.\\\\m_2=-\dfrac{1}{-\frac{5}{4}}=-\left(\dfrac{4}{5}\right)=\dfrac{4}{5}\\\\Answer:\ \boxed{D.\ \dfrac{4}{5}}[/tex]
