Answer:
The correct option is C.
Step-by-step explanation:
The given inequality is
[tex]6y-3x>9[/tex]
Isolate y on the left side in the above inequality.
[tex]6y>9+3x[/tex]
[tex]y>\frac{9+3x}{6}[/tex]
[tex]y>\frac{3}{2}+\frac{x}{2}[/tex]
If an inequality is defined as [tex]y\geq mx+b[/tex], then the shaded region is above the solid line.
If an inequality is defined as [tex]y\leq mx+b[/tex], then the shaded region is below the solid line.
If an inequality is defined as [tex]y>mx+b[/tex], then the shaded region is above the dashed line.
If an inequality is defined as [tex]y<mx+b[/tex], then the shaded region is below the dashed line.
Since the sign of inequality is >, therefore the shaded region is above the dashed line.
Hence option C is correct.
