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{1}{3}x+4\to m_1=-\dfrac{1}{3}[/tex]
Therefore
[tex]m_2=-\dfrac{1}{-\frac{1}{3}}=\dfrac{3}{1}=3[/tex]
We have the equation of a line:
[tex]y=3x+b[/tex]
Put the coordinates of the point (4, 3) to the equation of a line:
[tex]3=3(4)+b[/tex]
[tex]3=12+b[/tex] subtract 12 from both sides
[tex]-9=b\to b=-9[/tex]
Answer: y = 3x - 9
