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=-\dfrac{2}{3}x+5\to _1=-\dfrac{2}{3}[/tex]
Therefore
[tex]m_2=-\dfrac{1}{-\frac{2}{3}}=\dfrac{3}{2}[/tex]
We have the equation of a line: [tex]y=\dfrac{3}{2}x+b[/tex].
Put the coordinates of the point (8, 1) to the equation of a line:
[tex]1=\dfrac{3}{2}(8)+b[/tex]
[tex]1=(3)(4)+b[/tex]
[tex]1=12+b[/tex] subtract 11 from both sides
[tex]-11=b\to b=-11[/tex]
Answer: [tex]\boxed{y=\dfrac{3}{2}x-11}[/tex]
