The slope-point form: y - y₁ = m(x - x₁).
The slope-intercept form: y = mx + b.
[tex]k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
We have:
[tex]k:y-3=-4(x+2)\to m_1=-4[/tex] and the point (-5, 7)
therefore [tex]m_2=-\dfrac{1}{-4}=\dfrac{1}{4}[/tex]
[tex]y-7=\dfrac{1}{4}(x-(-5))\\\\\boxed{y-7=\dfrac{1}{4}(x+5)}\to\boxed{B.}[/tex]
