Write the inequality shown by the graph with the boundary line y = −x + 2.

Equation of line is, y = −x + 2

Graph:

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 equation of the line is,

y = -x + 2

It means this line divided the graph in to two part.

First one is y < -x + 2 and other is y > -x + 2.

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,

0 < 0 + 2 0 > 0 + 2

=> 0 < 2 => 0 > 2

We know that the 0 is less than 2.

It means the test point satisfied the inequality y < -x + 2.

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

Hence, the given graph is the graph of the inequality,

$y\le -x+2$

Hence, the given graph is the graph of the inequality$y\le -x+2$.