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Linear inequality in two variables x − y ≤ 5.

1) First change the inequality sign to equal and draw the boundary line.

If given inequality notation is > or < then draw the boundary line is dashed.

2) Choose test point that is not on the boundary line and check test point is solution of the given inequality or not.

3) Shade one side of the boundary line.

If test point is a solution of the given inequality then shade the part include the test point.

If test point is not solution of the inequality then shade the opposite part.

We have, x − y ≤ 5

To draw the line we can convert it to linear equation x − y ≤ 5.

Inequality contains the less than equal to notation so the boundary line is solid line.

It means all points on the boundary are satisfies the given inequality.

Line divides the graph in to two parts one is x − y < 5 and other is x − y > 5.

To shade the region we can choose the test point out side the boundary line.

Let us consider (0, 0) be the test point.

Substituting it in to the both inequality,

0 < 5 and 0 > 5

We know that 0 is less than 5.

It means test point satisfies the inequality

x − y < 5.

So we can draw the test point side part.

Therefore graph of the given inequality is,

Graph of the given two variable inequality

x − y ≤ 5 is,