Question

I need help with this problem , GEOMETRY

Answer 1

$k:\ y=m_1x+b_1\\l:\ y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1$

$1.\\(-6,\ 1),\ (0,\ -2)\\\\m_1=\dfrac{-2-1}{0-(-6)}=\dfrac{-3}{6}=-\dfrac{1}{2}\\\\(0,\ 3),\ (4,\ 1)\\\\m_2=\dfrac{1-3}{4-0}=\dfrac{-2}{4}=-\dfrac{1}{2}\\\\m_1=m_2\\\\Answer:\ Parallel$

$(-4,\ 0),\ (2,\ 4)\\\\m_1=\dfrac{4-0}{2-(-4)}=\dfrac{4}{6}=\dfrac{2}{3}\\\\(-3,\ 4),\ (1,\ -2)\\\\m_2=\dfrac{-2-4}{1-(-3)}=\dfrac{-6}{4}=-\dfrac{3}{2}\\\\m_1m_2=\dfrac{2}{3}\cdot\left(-\dfrac{3}{2}\right)=-1\\\\Answer:\ Perpendicular$