Slope of AB = (difference of y coords)/(difference of x coords)=(4-(-1))/(4-(-3))=5/7.
The slope of the perpendicular is the negative inverse of this slope=-7/5.
Equation in slope intercept form is y-4=(-7/5)(x-4).
Multiply through by 5: 5y-20=-7(x-4)=-7x+28, so -7x-5y=-48 is the equation of the perpendicular through B, answer C.