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=4x-3\to m_1=4[/tex]
Therefore
[tex]m_2=-\dfrac{1}{4}[/tex]
We have the equation of a line:
[tex]y=-\dfrac{1}{4}x+b[/tex]
Put the coordinates of the point (0, 7) to the equation of a line:
[tex]7=-\dfrac{1}{4}(0)+b\\\\\7=b\to b=7[/tex]
Answer: [tex]\boxed{y=-\dfrac{1}{4}x+7}[/tex]
