Let [tex]k:y=m_1x+b_1[/tex] and [tex]l:y=m_2x+b_2[/tex]
[tex]l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
We have
[tex]y=-2x-2\to m_1=-2[/tex]
Therefore
[tex]m_2=-\dfrac{1}{-2}=\dfrac{1}{2}[/tex]
We have the equation of a line:
[tex]y=\dfrac{1}{2}x+b[/tex]
Put the coordinates of the point (-2, 4) to the equation of a line:
[tex]4=\dfrac{1}{2}(-2)+b[/tex]
[tex]4=-1+b[/tex] add 1 to both sides
[tex]5=b\to b=5[/tex]
Answer: [tex]\boxed{y=\dfrac{1}{2}x+5}[/tex]
