Answer:
The slope of the line is [tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
For any line [tex]y=mx+b[/tex], a line that is perpendicular to it is [tex]y_\perp =-\frac{1}{m} x+b[/tex].
Therefore the slope of the perpendicular line is [tex]-\frac{1}{m}[/tex].
For our case [tex]y=\frac{3}{2}x-\frac{1}{2}[/tex] therefore the slope of the prependicular is the reciprocal of [tex]\frac{3}{2}[/tex] multiplied by [tex]-1.[/tex]
[tex]\therefore\:slope=-\frac{2}{3}.[/tex]
