Question

Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded? A. Above the solid line B. Below the solid line C. Above the dashed line D. Below the dashed line

Answer 1

The correct option is C.

Explanation:

The given inequality is

`6y-3x>9`

Isolate y on the left side in the above inequality.

`6y>9+3x`

`y>(9+3x)/(6)`

`y>(3)/(2)+(x)/(2)`

If an inequality is defined as
`y\geq mx+b`, then the shaded region is above the solid line.

If an inequality is defined as
`y\leq mx+b`, then the shaded region is below the solid line.

If an inequality is defined as
`y>mx+b`, then the shaded region is above the dashed line.

If an inequality is defined as
`y<mx+b`, 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.