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

x + y = −4.

We have given equation of the line is

x + y = -4 and graph is,

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.

Here we have given the equation of the line is,

x + y = -4

This line divided the graph into two parts.

First one is x + y > -4 and other is x + y < -4.

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 into both inequalities,

0 + 0 < -4 0 + 0 > - 4

=> 0 < -4 0 > -4

We know that 0 is grater than -4.

The test point satisfied the inequality $x+y\ge -4$.

We also have given the line is solid it means the points on the line is also the solution of this inequality.

Hence, given graph is the graph of the inequality$x+y\ge -4$.