Let's calculate the slope of the line with points (0,-1) and (3,1) (taken from the graph)
[tex]m=\frac{y2-y1}{x2-x1}=\frac{1-(-1)}{3-0}=\frac{1+1}{3}=\frac{2}{3}[/tex]
Since the slope of the line is 2/3, then the slope of a perpendicular line to it must be found with the formula:
m1*m2 = -1
(2/3)*m2= -1 (Replacing m1=2/3)
m2=-1/(2/3) (Dividing by 2/3 on both sides of the equation)
m2= -3/2 (Dividing fractions)
The answer is the option A, since the slope of that line is equal to -3/2.
