Answer:
1. perpendicular
2. parallel
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\\text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2[/tex]
[tex]1.\\f(x)=2x+3\to m_1=2\\\\g(x)=-\dfrac{1}{2}x+3\to m_2=-\dfrac{1}{2}\\\\m_1\neq m_2\\\\m_1m_2=(2)\left(-\dfrac{1}{2}\right)=-\dfrac{2}{2}=-1\\\\Answer:\ \text{lines are perpendicular}[/tex]
[tex]2.\\f(x)=\dfrac{1}{3}x+4\to m_1=\dfrac{1}{3}\\\\g(x)=\dfrac{1}{3}x+5\to m_2=\dfrac{1}{3}\\\\m_1=m_2\\\\Answer:\ \text{lines are parallel}[/tex]
