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{4}{5}x+3\to m_1=-\dfrac{4}{5}[/tex]
Therefore
[tex]m_2=-\dfrac{1}{-\frac{4}{5}}=\dfrac{5}{4}[/tex]
We have the equation of a line:
[tex]y=\dfrac{5}{4}x+b[/tex]
Put the coordinates of the point (4, 12) to the equation of the line:
[tex]12=\dfrac{5}{4}(4)+b[/tex]
[tex]12=5+b[/tex] subtract 5 from both sides
[tex]7=b\to b=7[/tex]
Answer: [tex]\boxed{y=\dfrac{5}{4}x+7}[/tex]
