Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x+4}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\===========================\\\\\text{We have}\ k:y=\dfrac{1}{2}x+5\to m_1=\dfrac{1}{2}\\\\\text{Let}\ l:y=m_2x+b.\\\\l\ \parallel\ k\iff m_2=m_1\to m_2=\dfrac{1}{2}.\\\\l:y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the given point (-4, 2) to the equation of a line:}\\\\2=\dfrac{1}{2}(-4)+b\\\\2=-2+b\qquad\text{add 2 to both sides}\\\\4=b\to b=4\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x+4[/tex]
