[tex]\text{The point-slope form}\\\\y-y_1=m(x-x_1)\\\\m-slope\\------------------------\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ l\iff m_1m_2=-1\\\\\text{We have}\\\\y-3=-4(x+5)\to m_1=-4\\\\y=mx+b\to-4m=-1\qquad\text{divide both sides by (-4)}\\\\m=\dfrac{1}{4}\\\\\text{We have the point (-5, 7) and the slope. Substitute:}\\\\y-7=\dfrac{1}{4}(x-(-5))\\\\Answer:\ \boxed{y-7=\dfrac{1}{4}(x+5)}\to\boxed{C.}[/tex]
