91Ó°ÊÓ

Here we have given inequality in two variables is$y>\frac{2}{5}x-4$.

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.

Here the line $y=\frac{2}{5}x-4$divides the graph in to two parts first part is $y<\frac{2}{5}x-4$and second is $y>\frac{2}{5}x-4$.

We have given inequality $y>\frac{2}{5}x-4$.

So the boundary of the graph is dashed line.

Now to draw region we will use the test point.

Let (0, 0) be the test point and which is not on the boundary line.

Substituting it in to both inequality,

$0<\frac{2}{5}\left(0\right)-4$ $0>\frac{2}{5}\left(0\right)-4$

0 < -4 0 > -4

We knw that the 0 > -4 it means the test point is the solution of inequality $y>\frac{2}{5}x-4$.

So just we will draw the test point side part.

Hence graph of the given inequality in two variables $y>\frac{2}{5}x-4$is,