The equation of line cd is (y-3) = - 2 (x-4). what is the slope of a line perpendicular to line cd?

Y-y1=m(x-x1)
slope is m

given
y-3=-2(x-4)
slope=-2

perpendicular lines have slopesthat multiply to -1

-2 times ?=-1
divide by -2
?=1/2

slope is 1/2

So the equation is in point slope form y-y1=m(x-x1) m=the slope so the slope of that equation is -2 the way how you would find the slop of the line that is perpendicular is you would take the negative reciprocal so that would be 1/2