Question

The equation of line CD is (y − 3) = − 2 (x − 4). What is the slope of a line perpendicular to line CD?

Answer 1

(y-3)=-2(x-4)
(y-3)= -2x+8
y= -2x+11
perpendicular slopes are always reciprocals and opposite so the slope would be
slope=1/2

Answer 2

$The\ slope-point\ form:y-y_0=m(x-x_0)\ where\ m\ is\ a\ slope\\\\If\ k:y=m_1x+b_1\ and\ l:y=m_2x+b_2\\\\k\perp l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\therefore\\the\ slope\ of\ line\ CD:y-3=-2(x-4)\ is\ m_1=-2\ and\ the\ slope\\of\ a\ line\ prpendicular\ to\ CD\ is\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}$

Answer: 1/2