Correct answer is C.
[tex]-x+2y=10
\\2y=x+10
\\y= \frac{1}{2} x+5
\\m_1= \frac{1}{2}
\\
\\6y=-12x+1
\\y=-2x+ \frac{1}{6}
\\m_2=-2
\\
\\m_1 \times m_2=\frac{1}{2} (-2)=-1 \Rightarrow \text{Lines are perpendicular}[/tex]
Therefore, lines are intersecting.