The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
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-3=-4(x+2)\to m_1=-4[/tex]
Therefore
[tex]m_2=-\dfrac{1}{-4}=\dfrac{1}{4}[/tex]
We have the slope and the point (-5, 7). Substitute to the point-slope formula:
[tex]y-7=\dfrac{1}{4}(x-(-5))\\\\\boxed{y-7=\dfrac{1}{4}(x+5)}[/tex]
