Answer:
[tex]\large\boxed{C.\ y=\dfrac{1}{2}x-5}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
[tex]\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff\ m_1m_2=-1\to m_2=\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]
Parallel line have the same slope.
Therefore a line parallel to the line [tex]y=\dfrac{1}{2}x+1[/tex] has equation
[tex]y=\dfrac{1}{2}x+b[/tex]
