First, let's find the slope of our line.
Remember that the product between lines that are perpendicular is -1.
This way,
[tex]\frac{3}{2}\cdot m=-1\rightarrow3m=-2\rightarrow m=-\frac{2}{3}[/tex]
Using the slope-point form,
[tex]y-0=-\frac{2}{3}(x+6)\rightarrow y=-\frac{2}{3}x-4[/tex]
Therefore, the line that passes through (-6,0) and that is perpendicular to y=(3/2)x is:
[tex]y=-\frac{2}{3}x-4[/tex]
Answer: Option B
