Write the inequality shown by the shaded region in the graph with the boundary line

$y=\frac{2}{3}x-3$

We have given graph with the boundary line $y=\frac{2}{3}x-3$.

Here we can use the test point to check the inequality.

Ax + By < C

Ax + By > C

Boundary line is Ax + By = C

Boundary line is not included in solution. Boundary line is dashed.

Ax + By ≤ C

Ax + By ≥ C

Boundary line is Ax + By = C

Boundary line is included in solution. Boundary line is solid.

We have given boundary line is $y=\frac{2}{3}x-3$

and given graph isThis line divided the graph in to the two parts one is $y<\frac{2}{3}x-3$and $y>\frac{2}{3}x-3$.

Now we can choose one point which is from the either left or right side of the line.

Suppose, test point: (0, 0)

Substituting this test point in to the both inequalities,

$y<\frac{2}{3}\left(0\right)-3$ $y>\frac{2}{3}\left(0\right)-3$

=> 0 < -3 0 > -3

False True

Inequality $y>\frac{2}{3}x-3$is true, the side of the line with (0, 0)

Therefore the shaded region shows the inequality shows the solution of inequality $y>\frac{2}{3}x-3$.

Since the boundary line is graphed with a solid line, the inequality includes the equal sign.

Therefore the graph shows the inequality$y\ge \frac{2}{3}x-3$

Hence the inequality $y\ge \frac{2}{3}x-3$is the solution of given graph