[tex]Let\ k:y=m_1x+b_1\ and\ l:y=m_2x+b_2,\ then:\\\\l\ ||\ k\iff m_2=m_1\\\\l\ \perp\ k\iff m_2m_1=-1\\---------------------------\\\text{We have}\\\\y=-2x+5\to m_1=-2\\\\y=\dfrac{1}{2}x+3\to m_2=\dfrac{1}{2}\\\\m_2\neq m_1\to \text{the lines are not parallel}\\\\m_2m_1=\dfrac{1}{2}(-2)=-1\to\text{the lines are perpendicular}\\\\Answer:\ \boxed{\text{The lines are perpendicular}}[/tex]
